Answer to Question #137054 in Discrete Mathematics for Kyle

Question

4. Suppose p is the statement 'I play softball' and q is the statement 'The moon is 250,000 miles from Earth.' Select
the correct statement corresponding to the symbols ┐p ∧ q.
A. I don't play softball and the moon is 250,000 miles from Earth.
B. It is not the case that either I play softball or the moon is 250,000 miles from Earth.
C. I don't play softball or the moon is 250,000 miles from Earth.
D. It is not the case that both I play softball and the moon is 250,000 miles from Earth.

5. Select the statement that is the negation of “Coach Spurrier is charming and Coach Spurrier is modest.”
A. Coach Spurrier is not charming and Coach Spurrier is not modest.
B. Coach Spurrier is not charming or Coach Spurrier is not modest.
C. Coach Spurrier is not charming and Coach Spurrier is modest.
D. Let’s get serious for a minute.

Answer 1

4. Suppose $p$ = 'I play softball' and $q$ = 'The moon is 250,000 miles from Earth.' Select the correct statement corresponding to the symbols $\neg p \wedge q$ .

Recall that $\neg$ denotes the nagation (not) and $\wedge$ denotes the conjunction (and). Therefore, we have the following statement:

A. I don't play softball and the moon is 250,000 miles from Earth.

5. Select the statement that is the negation of “Coach Spurrier is charming and Coach Spurrier is modest.”

Let p="Coach Spurrier is charming", q="Coach Spurrier is modest". Using de Morgan's law

$\neg(p \wedge q)= \neg p \vee \neg q$ we conclude that the nagation to “Coach Spurrier is charming and Coach Spurrier is modest” is

B. Coach Spurrier is not charming or Coach Spurrier is not modest.