Family Feud Review

Math 2200: Elementary Statistics

April 28, 2011

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Question 1

What is an equivalence relation?

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Answer 1

Answer

A relation R is an equivalence relation if R is reflexive, symmetric,and transitive.

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Question 2

Does there exist an equivalence relation R such that R is afunction? Give an example coinciding with your claim?

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Answer 2

Answer

Let R be a relation on the set A = {a, b} given byR = {(a, a), (b, b)}. Then R is an equivalence relation and R is afunction. This implies there does exist an equivalence relation thatis a function.

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Question 3

For the compound statement If P, then Q what truth valuesmust occur for statements P and Q in order for the implication tobe false.

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Answer 3

Answer

The statement P must be true and Q must be false.

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Question 4

Prove or disprove: If n N, then n2 n + 41 is prime.

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Answer 4

Answer

This statement is false since 412 41 + 41 = 412 is divisible by 41.

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Question 5

Give an indexed collection {Sr}rN of distinct sets (that is no twosets are equal) satisfying the conditions

rN

Sr = [0, 1] andrN

Sr = {0}.

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Answer 5

AnswerSr = [0,

1r ]

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Question 6

Determine if A B = A B. Give an example supporting yourclaim.

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Answer 6

Answer

Let U = {a, b}, A = {a}, B = {b}. Then A B = {(b, a)} andA B = {(a, a), (b, a), (b, b)}, which implies the two sets are notequal.

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Question 7

What does it mean for a function to be a bijection?

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Answer 7

AnswerA function is a bijection if the function is onto and an injection.

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Question 8

Give an example of infinite sets A and B along with a functionf : A B such that f is injective, but f is not onto.

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Answer 8

Answer

Let A = N and B = Z with f : N Z given by f (x) = x .

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Question 9

Let R be a relation on the set A = {a, b, c , d , e} given byR = {(a, c), (c , d), (d , c), (b, d), (e, c)}. Is R a function? Justifyyour answer.

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Answer 9

Answer

Yes, R is a function since every input has exactly one output.

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Question 10

Give an example of a relation R on the set A = {a, b, c , d , e} suchthat R is reflexive and transitive, but not symmetric.

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Answer 10

Answer

R ={(a, a), (b, b), (c, c), (d , d), (e, e), (a, d), (d , e), (a, e), (d , c), (a, c)}

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