Question

When using a counterexample to prove a conditional statement false, which must be true about the counterexample?

There must be infinite counterexamples.
The counterexample must satisfy the hypothesis of the conditional statement.
There must be at least one example under which the conditional statement is true.
The counterexample must satisfy the conclusion of the conditional statement.

Answer 1

The counterexample must satisfy the hypothesis of the conditional statement.

(Also note: to be a counterexample it must fail the conclusion — i.e., satisfy the hypothesis but not the conclusion.)