''If a zic is a zac, then a zic is not a zoc.''
If the statement above is true, then which of the following statements must also be true ?

Options

A. ''If a zic is a zoc, then a zic is not a zac.''
B. ''If a zic is not a zac, then a zic is a zoc.''
C. ''If a zic is not a zoc, then a zic is a zac.''
D. ''If a zic is not a zac, then a zoc is not a zac.''

Answer

A

Explanation

This example uses nonsense words to test your understanding of a basic rule of logic : Given a true statement, the statement's convers is not necessarily true, the statement's inverse is not necessarily true, but the statement's contrapositive must be true. That sounds like a mouthful, as you think about what follows, concern yourself not with fancy terminology such as inverse and converse - terms that won't appear on the test - but with the measnings of these terms.
The following statement is an if - them claim : If A, then B. The converse is what you get when you flip the if and the then : If B, then A. The inverse is what you get when you negate the if and the then : If not A, then not B. Finally, the contrapositive is what you get when you both flip and negate the A and the B : If not B, then not A. Again, given a true statement, the statement's contrapositive must follow.
Consider an example : If I am in lowa, then I am in the United States. The converse of this statement is : If I am in the United States, then I am in lowa. Is it possibly true that a person in he United States is in lowa ? Yes. Is it necessarily true ? No. The inverse of the original statement is, If I am not in lowa, then I am not in the United States. Is it possibly true that a person not in lowa is not in the United States ? Yes. Is it necessarily true ? No. Now consider the contrapositive of the original statement : If I am not in the United States, then I am not in lowa. Not only is it possible that a person not in the United States not be in lowa, but it is necessarily true that someone not in the United States is not in lowa. From the Contrapositive by both flipping and negating the if and the then. Flipping them produces, If a zic is not a zoc, then a zic is a zac. Now negate the terms : If a zic is a zoc, then a zic is not a zac. The answer is (A).