Answer: It's a matter of knowing what those words and symbols mean. Read and learn.
Explanation:
Statement 1 is "A⇒B" or "A=>B". It can be read as "A implies B", or "If A then B", or "B only if A." It is also the same as "B or not A," but that is written "B ∨ ¬A" or "B || ~A".
Statement 2 is "B⇒A" or "B=>A". It can be read as "B implies A", or "If B then A", or "A only if B". It is also the same as "A or not B," but that is written "A ∨ ¬B" or "A || ~B".
Choice "D. Contradiction": Eliminated, since statement 2 does not contradict statement 1.
The statement which contradicts "A implies B" is "A does not imply B", or "not (B or not A)" which expands to "A and not B" by DeMorgan's theorem. You must have B false and A true to contradict "A implies B."
Choice "A Inverse": Eliminated for the same reason as choice D.
The "inverse" or "negation" of a logical statement is true whenever the original statement is false, and vice versa. That is to say, one statement is the inverse of another if and only if the two statements contradict one another. Here, statement 2 is not the negation of statement 1. "B implies A" is not the same as "A does not imply B."
Choice "B Contrapositive":
The contrapositive of "A implies B" is "(not B) implies (not A)", or "¬B⇒¬A". The two, "A⇒B" and "¬B⇒¬A", are equivalent: both are true unless B is false and A is true. "A implies B" means "B or not A".
"Not B implies not A" means "not A or not not B," which is the same as "B or not A".
This leaves choice "C: converse" as the correct answer. The converse of statement 1, "A implies B", is "B implies A". When both are true, we say "A if and only if "B.