Proof Techniques and Notes

Question 1

direct proof

Answer 1

most straight forward and basic method

Question 2

proof by exhaustion

Answer 2

check all cases

Question 3

WLOG

Answer 3

without loss of generality

Question 4

proof by contraposition

Answer 4

P => Q is equivalent to ~Q => ~P. Best used if higher degree => lower degree. Must state “by contraposition.”

Question 5

proof by contradiction

Answer 5

Assume P is false. Deduce some proposition Q. Also deduce ~Q. Conclude that P must have been true. Must state “this contradiction implies.”