For some integers that are not palindromes, like 91, a person can create a palindrome by repeatedly reversing the number and adding the original number to its reverse. for example, $91 + 19 = 110$. then $110+011 = 121$, which is a palindrome, so 91 takes two steps to become a palindrome. of all positive integers between 10 and 100, what is the sum of the non-palindrome integers that take exactly six steps to become palindromes?

Answers

Answer 1

The sum of non- palindrome integer is b

What is Palindrome number?

A palindromic number is a number that remains the same when its digits are reversed.

Given:

$91 + 19 = 110$. then $110+011 = 121$

So, there are two numbers which needed 6 steps to become a palindrome number

First, 79

79 +97

=176 + 671

=847 + 748

=1,595 + 5,951

=7,546 + 6,457

=14,003 + 30,041

=44,044

and, the second number is

97 + 79=176

176+671=847

847+ 748= 1595

1,595 + 5,951 = 7,546

7,546 + 6,457 = 14,003

14,003 + 30041

= 44044

Hence, the sum of digits is 16.

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Related Questions

\(2x^2-20x=x^{2} -19\)

Answers

Answer:

x = 1, x = 19

Step-by-step explanation:

Given

2x² - 20x = x² - 19 ( subtract x² - 19 from both sides )

x² - 20x + 19 = 0 ← in standard form

(x - 1)(x - 19) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 19 = 0 ⇒ x = 19

x1 = 1 x2 = 19 if I’m correct

Jennifer went to a farm and bought tomatoes
for $2 per pound and garlic for $3 per pound.
If Jennifer spent $72 on tomatoes and garlic,
how many pounds can she buy if she buys
only garlic?

Answers

Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

What is a pound defined as?

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

What is a division example?

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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Ireland owes her dad $100. She plans on paying him $20 per week until it is paid off.

Answers

Answer:

5 weeks

Step-by-step explanation:

I believe your looking for the time it will take her to pay it off.


Determine which data set best corresponds to the given scatter plot.

Determine which data set best corresponds to the given scatter plot.

Answers

Answer:

Are there any options?

and it's not A)

so B)

Step-by-step explanation:

(1 point) Find the angleαin radians between the vectors[−12​] and [6−1​]α=

Answers

The angle between the vectors "[−12​] and [6−1​]α" is approximately 2.03 radians.

To find the angle between the vectors, we can use the formula:

cos(α) = (\(V{1}\) • \(V{2}\)) / (||\(V{1}\)|| ||\(V{2}\)||)

Where v1 and v2 are the two vectors, and ||\(V{1}\)|| and ||\(V{2}\)|| are the magnitudes of the vectors.

For the given vectors:

\(V{1}\) = [−1 2] and \(V{2}\) = [6 −1]

\(V{1}\)• v2 = (−1)(6) + (2)(−1) = −6 + −2 = −8

||\(V{1}\)|| = √((-1)^2 + 2^2) = √(5)

||\(V{2}\)|| = √(6^2 + (-1)^2) = √(37)

cos(α) = (−8) / (√(5) √(37)) = −8 / √(185)

α = cos^-1(−8 / √(185))

α ≈ 2.03 radians

Therefore, the angle between the vectors is approximately 2.03 radians.

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Use the given information to find the p-value. also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). with h1: p(=/)4/5, the test statistic is z=1.52
1)0.0643; reject the null hypothesis
2)0.0643; fail to reject eh null hypothesis
3)0.1286; reject the null hypothesis
4)0.1286; fail to reject the null hypothesis

Answers

The correct option is: 4) 0.1286; fail to reject the null hypothesis.

Given h1: p(=/)4/5 and the test statistic is z = 1.521.

Also, we need to use a 0.05 significance level.

The formula to calculate the p-value is:

P-value = P(Z > 1.521) + P(Z < -1.521)

P-value = P(Z > 1.521) + P(Z > 1.521) [because Z-distribution is symmetrical]

P-value = 2 * P(Z > 1.521)

To find the p-value, we can use a standard normal table or calculator.Using standard normal distribution table, we get:

P(Z > 1.521) = 0.0636

Therefore, the p-value is 2 * 0.0636 = 0.1272.

Since the p-value (0.1272) is greater than the level of significance (0.05), We are unable to rule out the alternative.

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PLEASE HELP ASAP! WILL GOVE BRAINLIEST!!! I NEED THIS DONE PLEASE FOLLOW DIRECTIONS!

PLEASE HELP ASAP! WILL GOVE BRAINLIEST!!! I NEED THIS DONE PLEASE FOLLOW DIRECTIONS!

Answers

Answer:

I'm not sure but

Step-by-step explanation: The area is 9.5 feet.

describe system of linear equations using practical situation and mathematical expressions

pahelp pooo​

Answers

Answer:

A system of linear equations is a collection of two or more linear equations, and a solution to a system of linear equations consists of values of each of the unknown variables in the system that satisfies all of its equations, or makes them true.

HELP ASAP! which pairs of the angles in the figure below are vertical angles?

HELP ASAP! which pairs of the angles in the figure below are vertical angles?

Answers

Answer:

B, C

Step-by-step explanation:

Seeing as you said ASAP I thought I wouldn't spend time writing an explanation, but let me know if you do want one.

Answer:  B

Step-by-step explanation:each of the pairs of opposite angles made by two intersecting lines.

Who can help me please

Who can help me please

Answers

The similarity statements are;

SV/RS = TV/TU

AC/AB = CE/ED

What are similar triangles?

Formally, two triangles ABC and DEF are similar if and only if:

Their corresponding angles are congruent, meaning that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.

The corresponding sides are in proportion to each other, meaning that the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, which is also equal to the ratio of the length of side AC to side DF.

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An individual can win a bouncy ball by guessing under which one of four cups the ball is located. After each guess, if the ball is won, a new ball is placed randomly under one of the four cups. If the ball is not won, then the ball is again placed randomly under one of the four cups. If an individual makes five guesses, what is the probability the individual will win a prize exactly two times?

Answers

The probability of winning a bouncy ball exactly two times in five guesses is 0.1324 or about 13.24%.

Explanation:

We can do this using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

X is the number of successes (i.e., winning the bouncy ball), n is the number of trials (i.e., number of guesses), p is the probability of success (i.e., finding the ball under the cup), and k is the number of successes we're interested in (i.e., 2 in this case).

In this scenario, n = 5 and we need to find p.

To find p, we need to consider each guess separately. For the first guess, the probability of winning is 1/4. If the first guess is incorrect, then the ball is randomly placed under one of the cups again, and the probability of winning on the second guess is also 1/4. Similarly, for the third, fourth, and fifth guesses, the probability of winning is 1/4. So, the overall probability of winning exactly 2 times in 5 guesses is:

P(X = 2) = (5 choose 2) * (1/4)^2 * (3/4)^3

= (10) * (1/16) * (27/64)

= 0.1324

Therefore, the probability of winning a bouncy ball exactly two times in five guesses is 0.1324 or about 13.24%.

Starting with a list of the three numbers, the "changesum" procedure creates a new list by replacing each number with the sum of the other two. For example, from {3, 4, 6} the procedure "changesum" gives {10, 9, 7} and a new "changesum" leads to {16, 17, 19}. If we begin with the list {20, 1, 3}, what is the maximum difference between two numbers of the list after 2013 consecutive "changesums"?

Answers

After 2013 "changesums", the list {20, 1, 3} becomes {x, x, x}. The maximum difference between two numbers is 0 since all numbers are equal.

We can start by applying the "changesum" procedure to the list {20, 1, 3} repeatedly, until we have done it 2013 times.

After the first application, we get the list {4, 23, 21}. After the second application, we get {44, 25, 27}. We can continue applying the procedure to get the following list of values:

{44, 25, 27}

{69, 71, 52}

{142, 120, 140}

{262, 282, 262}

{524, 524, 544}

{1048, 1068, 1048}

{2116, 2096, 2116}

{4212, 4232, 4212}

After 2013 consecutive "changesums", the list will have the form {x, x, x} for some value x. The maximum difference between two numbers in the list will be 0 in this case, since all the numbers are equal.

Therefore, the maximum difference between two numbers of the list after 2013 consecutive "changesums" is 0.

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PLEASE HELP!!!:)). The area of ​​the trampezoid is 100dm and the bases are 2.1m and 1.9m. Calculate the height of the trampezoid .

Answers

Answer:

Well, the only thing you should do is to use the formula.

if the bases are: a, b

and the height is=h

Then, this is your formula, S=½(a+b)×h

Step-by-step explanation:

Aight,

100dm=10m

S=10m

now, the formula

10=½(2.1+1.9)×h===> 20=4h==> h=5m

Marry takes \( k \) minutes to finish a math assignment. David takes \( k-5 \) minutes to finish an assignment. They take 30 minutes when working together. a) How long does each person take? T4]

Answers

The answer to this question is:Marry takes 35/2 minutes and David takes 25/2 minutes to complete the assignment.

Let the time Marry takes to complete the math assignment be k minutes time David takes to complete the math assignment be k - 5 minutes

It is given that when they work together, they complete the math assignment in 30 minutes.Using the concept of efficiency, we can say that time taken by Marry alone + Time taken by David alone = Time taken when they work together in minutes

Equation becomes:

k + k - 5 = 30

Simplifying the equation gives:

2k = 35k = 35/2

Substituting the value of k in the expression k - 5 to find the time taken by David alone we get:

k - 5 = 35/2 - 5

= 25/2

Thus, it can be concluded that Marry takes 35/2 minutes (17.5 minutes) and David takes 25/2 minutes (12.5 minutes) to complete the math assignment. Therefore, the answer to this question is:

Marry takes 35/2 minutes and David takes 25/2 minutes to complete the assignment.

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Someone help me please!

Someone help me please!

Answers

Answer:

A: the scale is missing



i hope this helps

Step-by-step explanation:

Answer:

the numbers are supposed to start at zero and the scale is missing

a particle is moving with the given data. find the position of the particle. a(t) = cos(t) sin(t), s(0) = 2, v(0) = 1

Answers

The required answer is s(t) = -0.125 sin(2t) + 1.25t + 2.

Explanation:-

To find the position of the particle,  to integrate the acceleration function twice with respect to time.

Given:

a(t) = cos(t) sin(t)

s(0) = 2 (initial position)

v(0) = 1 (initial velocity)

To integrate a(t) with respect to t, first find the antiderivative of a(t):

∫a(t) dt = ∫cos(t) sin(t) dt

rewrite cos(t) sin(t) as 0.5 sin(2t), using the identity sin(2t) = 2 sin(t) cos(t):

∫a(t) dt = ∫0.5 sin(2t) dt

Using the integral of sin(2t), we have:

∫a(t) dt = -0.25 cos(2t) + C1

Now, apply the initial velocity condition:

v(0) = 1

At t = 0, the velocity is given as 1. Substituting this into the equation:

-0.25 cos(2*0) + C1 = 1

-0.25(1) + C1 = 1

C1 = 1.25

Now, the first integration:

∫a(t) dt = -0.25 cos(2t) + 1.25

To find the position function s(t),  integrate ∫a(t) dt with respect to t:

∫∫a(t) dt dt = ∫(-0.25 cos(2t) + 1.25) dt

Integrating,

∫∫a(t) dt dt = -0.125 sin(2t) + 1.25t + C2

Applying the initial position condition:

s(0) = 2

At t = 0, the position is given as 2. Substituting this into the equation,  

-0.125 sin(2*0) + 1.25(0) + C2 = 2

C2 = 2

Therefore, the position function is:

s(t) = -0.125 sin(2t) + 1.25t + 2.

This equation represents the position of the particle as a function of time, given the initial conditions.

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someone please help...​

someone please help...

Answers

Answer:

2 1/3

1 4/3

2.333...

233.3...%

Step-by-step explanation:

Select all choices that have supplementary angles.

O ZAFE and ZDFE
OZCFD and ZEFD
OZAFB and BFD
OZAFC and ZEFD
OZAFE and ZCFD
OZAFB and BFC

Select all choices that have supplementary angles.O ZAFE and ZDFEOZCFD and ZEFDOZAFB and BFDOZAFC and

Answers

Based on the information we can infer that the complementary angles are those of options A, B, and C.

How to identify complementary angles?

To identify complementary angles we must take into account that they must add up to 180°. In this case we do not have the measures of the angles but we know that an angle of 180° is a straight line, so the complementary angles would be those that form a straight line.

According to the above, the complementary angles of this graph would be:

AFE and DFECFD and EFDAFB and BFD

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what results In ridge regression, choosing a very large \lambdaλ penalty strength

Answers

In ridge regression, the penalty strength parameter, represented by \lambda», controls the trade-off between fitting the training data well and keeping the model coefficients small.

When a very large penalty strength is chosen, it results in a higher degree of shrinkage of the regression coefficients towards zero. This means that the model becomes less complex and less likely to overfit the training data. However, it also means that the model may become too biased towards the null hypothesis, leading to underfitting and decreased predictive power. Therefore, choosing the right value of \lambdaλ is crucial for achieving optimal performance in ridge regression.
In ridge regression, choosing a very large λ (lambda) penalty strength results in a higher regularization effect, which helps to reduce overfitting by shrinking the coefficients of the independent variables towards zero. This helps to create a more generalized model by controlling the complexity of the model. However, choosing a λ value that is too large can also result in underfitting, as the model may become too simple to capture the underlying relationships in the data effectively.

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If Var(X)=10,Var(Y)=15 and Cov(X,Y)=−7, what is Var(2X+3Y)= ? Answer: Assume that we have a Bernoulli random variable with parameter p=0.3. What is its expected value? What is its variance?

Answers

The expected value of the Bernoulli random variable is 0.3 and its variance is 0.21.

To find Var(2X + 3Y), we can use the properties of variance and covariance:

Var(2X + 3Y) = Var(2X) + Var(3Y) + 2Cov(2X, 3Y)

Since X and Y are independent random variables, Cov(X, Y) = 0.

Var(2X) = 2^2 * Var(X) = 4 * 10 = 40

Var(3Y) = 3^2 * Var(Y) = 9 * 15 = 135

Therefore,

Var(2X + 3Y) = Var(2X) + Var(3Y) + 2Cov(2X, 3Y) = 40 + 135 + 2 * 2 * 3 * 0 = 40 + 135 = 175

So, Var(2X + 3Y) = 175.

For the Bernoulli random variable with parameter p = 0.3:

The expected value (mean) of a Bernoulli random variable is given by E(X) = p. Therefore, E(X) = 0.3.

The variance of a Bernoulli random variable is given by Var(X) = p(1 - p). Therefore, Var(X) = 0.3(1 - 0.3) = 0.3(0.7) = 0.21.

So, the expected value of the Bernoulli random variable is 0.3 and its variance is 0.21.

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help asap!!!!!!!!!!!

help asap!!!!!!!!!!!

Answers

There are 24 different ways to arrange the cards in the boxes.

How to arrange the card in the box?

Because there are four boxes and four cards, there are four ways to arrange the first card, three ways to arrange the second card (because one box is already occupied), two ways to arrange the third card, and one method to arrange the fourth card. As a result, the total number of possible ways to arrange the cards in the boxes is:

4 x 3 x 2 x 1 = 24

So there are 24 different ways to arrange the cards in the boxes.

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Decimal Addition/Subtraction.

Decimal Addition/Subtraction.

Answers

Answer:

D. 1.175L

Step-by-step explanation:

If a rectangle has a width of 36 square units, is it inversely proportional to its width?
Please explain.

Answers

Answer:

tegf ehetrh

Step-by-step explanation:

rwh rt  hre r

On a coordinate plane, line A B goes through (negative 4, 0) and (2, negative 3). Point C is at (negative 2, 2).
Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?

Answers

The point on the x-axis that lies on the line passing through point C and parallel to line AB is (4, 0).

How to find the points that are parallel

A line that is parallel to line AB and passes through point C has the same slope as line AB. The slope of line AB can be found using the formula:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

In this case, (x1, y1) = (negative 4, 0) and (x2, y2) = (2, negative 3).

Substituting these values into the formula, we get:

m = (-3 - 0) / (2 - -4) =  -3 / 6 = -1/2

Since the slope of line AB is -1/2,

the slope of the line through point C and parallel to line AB is also -1/2.

A line with slope -1/2 and passing through (negative 2, 2) has the equation:

y - 2 = -1/2 (x - -2),

Rearranging this equation to solve for y, we get:

y = -1/2 x + 2

The x-axis has y-coordinate 0, so substituting 0 for y in the equation, we get:

0 = -1/2 x + 2

Solving for x, we get:

x = 4

hence the point is (4, 0)

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the arithemtic mean of a set of 20 test scores is represented by x. if each score is increased by y points, which expression represents the airthmetic mean of the revised set of test scores

Answers

The arithmetic mean of the revised set of test scores, after each score is increased by y points, is represented by (x + y).

Let's assume the original set of test scores is denoted by {x₁, x₂, x₃, ..., x₂₀}, and the arithmetic mean of these scores is represented by x.

To find the arithmetic mean of the revised set of test scores, where each score is increased by y points, we need to add y to each score and calculate the new mean.

The revised set of test scores would be {x₁ + y, x₂ + y, x₃ + y, …, x₂₀ + y}.

To calculate the arithmetic mean of the revised set, we sum up all the revised scores and divide by the total number of scores:

Arithmetic mean of revised set = (x₁ + y + x₂ + y + x₃ + y + … + x₂₀ + y) / 20

= (x₁ + x₂ + x₃ + … + x₂₀) / 20 + (y + y + y + … + y) / 20

= x / 20 + (20y) / 20

= x / 20 + y

Therefore, the expression that represents the arithmetic mean of the revised set of test scores is (x + y).

When each score in a set of 20 test scores is increased by y points, the arithmetic mean of the revised set can be represented by (x + y), where x represents the original arithmetic mean of the scores and y represents the increase in points for each score.

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Select the correct anwer. What i the value of thi expreion when c = -4 and d = 10?
A. 2
B. 9
C. 21
D. 41
Reet

Answers

The expression be 1/4(c³+ d²) then the value exists 9.

What is meant by PEMDAS order of operations?

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right).

The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations.

Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).

Let the given expression be 1/4(c³+ d²)

The value of c = -4 and d = 10

substitute the values in the above equation, we get

Follow the PEMDAS order of operations

Calculate within parentheses  ((-4)³ + (10)²) = 36

1/4((-4)³ + (10)²)

simplifying the above equation, we get

= 1/4 × 36

= 9

Therefore, the correct answer is option B. 9.

The complete question is:

What is the value of this expression when c = -4 and d = 10?

1/4(c³+ d²)

A. 2

B. 9

C. 21

D. 41

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A radioactive substance decays exponentially. A scientist begins with 200 milligrams of a radioactive substance. After 36 hours, 100 mg of the substance remains. How many milligrams will remain after 52 hours

Answers

After 52 hours, approximately 70.7 milligrams of the radioactive substance will remain.

To solve this problem, we can use the exponential decay formula:
N(t) = N0 * e^(-λt)
where N(t) is the amount of substance remaining at time t, N0 is the initial amount of substance, λ is the decay constant, and e is the base of the natural logarithm.
We can find λ by using the fact that half of the substance decays in 36 hours:
N(36) = N0/2
100 mg = 200 mg * e^(-λ * 36)
e^(-λ * 36) = 0.5
-λ * 36 = ln(0.5)
λ = ln(2)/36
Now we can use this value of λ to find N(52):
N(52) = 200 mg * e^(-λ * 52)
N(52) = 200 mg * e^(-ln(2)/36 * 52)
N(52) ≈ 78.1 mg
Therefore, approximately 78.1 milligrams of the radioactive substance will remain after 52 hours.
A scientist is observing a radioactive substance that decays exponentially. Initially, there are 200 milligrams of the substance. After 36 hours, 100 milligrams remain. To determine how many milligrams will remain after 52 hours, we can use the formula:
Final amount = Initial amount * (1/2)^(time elapsed/half-life)
First, we need to find the half-life of the substance. Since it decays to half its initial amount in 36 hours:
Half-life = 36 hours
Now we can plug in the values to find the amount remaining after 52 hours:
Final amount = 200 mg * (1/2)^(52/36) = 200 mg * (1/2)^1.44 ≈ 70.7 mg
After 52 hours, approximately 70.7 milligrams of the radioactive substance will remain.

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Compare and contrast angular momentum and linear momentum. Include two ways that they are alike and two ways that they are different. Be sure to discuss how mass affects both angular and linear momentum. (5 points)

Answers

Answer:

Linear momentum of an object is the product of the object’s mass and velocity. Linear momentum is a vector quantity, and the direction of momentum is taken to be the direction of the object’s velocity.

or an object with mass  moving at a velocity , the angular momentum  with respect to a reference point is defined using the cross product as:

where  is the position vector of the object that describes the object’s position with respect to the reference point. The units for measuring angular momentum is kg m2 s-1. Since angular momentum is defined in terms of a cross product, the direction of the angular momentum vector is taken to be in a direction perpendicular to both the particle’s position vector  and its velocity vector

Step-by-step explanation:

AB is parallel to CD. CD is rotated 180° Which statement describes the relationship between ('D' and the transformed AB? How can
you prove it?

Answers

Answer:

Answer :- Statement (B) ,C'D' ll AB

Given AB is parallel to CD.  CD rotated.

Consider a transversal line l intersecting AB and CD at angle x.

therefore By slope formula,

slope of AB and CD = m =tanx

Now after rotation of 180 CD become C'D'

therefore, slope of C'D' = =tanx=m

Hence C'D' ll AB.

Given the following relations on the set of all people. Check ALL correct answers from the following lists:
(a) a is (strictly) older than b
A. irreflexive
B. symmetric
C. antisymmetric
D. reflexive
E. transitive
(b) a and b have a common grandparent
A. irreflexive
B. antisymmetric
C. symmetric
D. reflexive
E. transitive
(c) a has the same first name as b
A. transitive
B. irreflexive
C. antisymmetric
D. symmetric
E. reflexive
(d) a and b were born on the same day
A. transitive
B. reflexive
C. irreflexive
D. antisymmetric
E. symmetric

Answers

The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.

irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.

The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.

This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:

This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.

(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.

The correct answers for each given relation are listed above.

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