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3. discrete math question 1 give a counterexample to the following...

# Question: discrete math question 1 give a counterexample to the following...

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Discrete Math

Question 1: Give a counterexample to the following using explicit values for a,b,c. Carefully explain why each part holds or fails.

Suppose that gcd(a,b) = 1 and gcd(a,c) = 1. Then gcd(b, c) = 1

Question 2: Prove: If a|b and c|d, then ac|bd.

Question 3: Prove: If k|n and a ≡ b mod n, then a ≡ b mod k.