Question

foundations of euclidean geometry
when using a counterexample to prove a conditional statement false, which must be true about the counterexample?
there must be at least one example under which the conditional statement is true.
the counterexample must satisfy the conclusion of the conditional statement.
the counterexample must satisfy the hypothesis of the conditional statement.
there must be infinite counterexamples.

Explanation:

A counter - example to a conditional statement "if p then q" (where p is the hypothesis and q is the conclusion) is an example where the hypothesis p is true, but the conclusion q is false. So, the counter - example must satisfy the hypothesis of the conditional statement.

Answer:

The counterexample must satisfy the hypothesis of the conditional statement.