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Proofs%20To%20Critique%201

# Proofs%20To%20Critique%201 - Proof 3 1 Assume a | b This...

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MA 315, Spring 2011 Proofs To Critique Critique the following proofs line by line. For each line, you should state whether the line is correct or not. In addition, state whether the line is needed or not. Can any of the lines be improved? Theorem: If a , b and c are integers and a | b , then a | ( bc ). Proof 1: 1. We know that a | b , so ak = b . 2. Multiply a | b by c to get a | ( bc ). This is what we had to prove. Proof 2: 1. Let a , b , c and k be integers. Let a | b . This means that b/a = k . 2. Multiply both sides by c to get bc/a = kc . Since kc is an integer, bc is divisible by a which is what we had to prove.

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Unformatted text preview: Proof 3: 1. Assume a | b . This means that b/a = k for some integer k . This also means that ak = b . This means we can also say that b is divisible by a . 2. Since b is divisible by a , any multiple of b is divisible by a . Therefore, bc is divisible by a . This is what we had to prove. 1 Proof 4: 1. Since a | b is deﬁned, we can say ak = b for some integer k . 2. Multiply both sides to obtain akc = bc . 3. This shows that a | bc and a | b . 2...
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