prositional logic

Question

what is the difference BETWEEN "IF" and "ONLY IF" when we translate an english sentence into a logical expression???

Answer 1

A if B is B implies A

A only if B is A implies B

A if and only if is  A is equivalent to B

Answer 2

If A Then B means A Implies B

B, IF A means A implies B

B ONLY IF A means B Implies A

You can actually compare ONLY IF == Then .

A IF & ONLY IF B => A=B