Proves by Contrapositive

Question 1

Steps to prove by contrapositive?

Answer 1

*State a fact: if a is small, then b is big.
*Identify a contrapositive: if b is small, then a is not small.
*State a mathematical fact that defines the property of the variables: small and big.
*Start the proof assuming that b is the opposite: b is small.
*End the proof proving that a is not small.

Question 2

Truth table (p -> q)?

Answer 2

Refer to page 9 of textbook

Question 3

a and b are congruent modulo when? (a = b (mod n)).

Answer 3

n is a factor of a and b (n | (a - b) when n is an element of the natural numbers.

Question 4

Worded definition of congruent modulo in terms of a and b when divided by n?

Answer 4

When an and b both have the same remainder when divided by n. Thus (a - b)/n -> (a/n) - (b/n) in which both a/n and b/n have the same remainder.