Equivalence between two statements. ‘If A then B’ means A is a sufficient condition for B and B is a necessary condition for A. ‘If B then A’ means B is a sufficient condition for A and A is a necessary condition for B. Both statements being true implies ‘A if and only if B’ (written ‘A iff B’) which means that each of A and B is a necessary and sufficient condition for the other; either both are true or both are false. The two statements are thus equivalent.