A counterexample disproves a statement by giving a situation where the statement is false; in proof by contradiction, you prove a statement by assuming its negation and obtaining a contradiction.

How do you disprove a statement in discrete mathematics?

Disprove by counterexample that for any a , b ∈ Z , if a 2 = b 2 , then a = b . Note that Z is the set of all positive or negative integers. Finding an a and b such that a ≠ b but a 2 = b 2 , then the statement is disproved. Choosing any integer for a and then choosing b = − a will accomplish this.

How many counterexamples are needed to disprove a statement?

Two counterexamples are needed to prove a statement is false.