MathMaster Blog

Example 1:

If P implies Q, an equivalent statement is:

1. Q implies P
2. Q is a necessary condition for P
3. P is a necessary condition for Q
4. Not P implies Q
5. Nor P implies not Q

Solution:

The converse, inverse, and negative are not equivalent statements. The contrapositive,～Q→～P, is equivalent and this is the same as saying that Q is a necessary condition for P. So, the answer is B.

Example 2:

Determine whether each set is well defined:

1. The set of dog breeds that are cute.
2. The set of women who have won the United States Open Tennis Championship.

Solution:

1. Not defined because cuteness is subjective.
2. Defined because there is a limited number of champions.