Proofs%20To%20Critique%201

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 dened, 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...
View Full Document

This note was uploaded on 02/16/2011 for the course MA 315 taught by Professor Peterturbek during the Spring '11 term at Purdue University Calumet.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online