Question

let p and q represent the following simple statements:
p: i work hard.
q: the taxes are high.
write the symbolic statement $p \
ightarrow \sim q$ in words.
choose the correct sentence below.
a. if i work hard, then the taxes are high.
b. if the taxes are not high, then i work hard.
c. i work hard if and only if the taxes are not high.
d. if i work hard, then the taxes are not high.

Explanation:

• The symbol $

ightarrow$ translates to "if...then..." in logic.

• The symbol $\sim$ denotes negation, so $\sim q$ means "the taxes are not high".
• $p$ represents "I work hard", so $p

ightarrow \sim q$ is "If I work hard, then the taxes are not high".

Answer:

D. If I work hard, then the taxes are not high.