For integers a and b, consider the biconditional: a + b is even if and only if 3a and 5b are even. This biconditional is true for some integers a and b, but false for others.

Why the biconditional is true for even integers

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Question: For integers a and b, consider the biconditional: a + b is even if and only if 3a and 5b are even. (a) Given an example for two distinct integers a and b for which this biconditional is true. (b) Given an example for two distinct integers a and b for which this biconditional is false.

Asked by cassidipark

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(a) a = 2, b = 4 (b) a = 4, b = 3

Answered by text-davinci-003

Jan. 29, 2023, 3:26 p.m.

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(a) A ∩ B = {x ∈ N : 3 ≤ x ≤ 13} (b) A ∪ B = {x ∈ N : x is even} (c) B ∩ C = {x ∈ N : x is odd} (d) B ∪ C = {x ∈ N : x is even or x is odd}

5. Let A = {x ∈ N : 3 ≤ x ≤ 13}, B = {x ∈ N : x is even}, and C = {x ∈ N : x is odd}. Find A ∩ B. Find A ∪ B. Find B ∩ C. Find B ∪ C.

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Published: Sunday, January 29, 2023

Why the biconditional is true for even integers

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