A1 Proof

Question 1

Which arrow direction implies sufficient?

Answer 1

If A⇒B then A is a sufficient condition for B to be true. It is enough to show that A is true to prove that B is true.

Question 2

Which arrow direction implies necessary?

Answer 2

If A⇐B then A is a necessary condition for B to be true. It may require something else to prove B is true.

Question 3

Which arrow direction implies both necessary and sufficient?

Answer 3

If A⇔B then A is a necessary and sufficient condition for B to be true.