This example uses nonsense words to test your understanding of a basic rule of logic: Given a true
statement, the statement’s converse 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 meanings of these terms.
The following statement is an if-then 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 Iowa, then I am in the United States. The converse of this statement
is: If I am in the United States, then I am in Iowa. Is it possibly true that a person in the United States
is in Iowa? Yes. Is it necessarily true? No. The inverse of the original statement is, If I am not in Iowa,
then I am not in the United States. Is it possibly true that a person not in Iowa 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 Iowa. Not only is it possible that a person not in the
United States not be in Iowa, but it is necessarily true that someone not in the United States is not
in Iowa.
1. “If a zic is a zac, then a zic is not a zoc.”2. If the statement above is true, then which of the following statements must also be true?(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.”(E) “If a zoc is a zic, then a zac is a zic.”