Question

use the equivalency

\\(\sim(p \
ightarrow q) \equiv p \wedge \sim q\\)

to select the statement that is logically equivalent to the negation of the conditional statement.....

\if a fruit is blue, then it is not a banana.\

• a fruit is not blue, or it is not a banana
• a fruit is not blue, and it is a banana
• a fruit is blue, and it is not a banana
• a fruit is not blue, and it is not a banana
• if it is a banana, then a fruit is not blue
• if a fruit is not blue, then it is a banana
• a fruit is blue, and it is a banana
• if it is not a banana, then a fruit is blue

Explanation:

Define symbolic representations

$$
LATEXBLOCK0
$$

Apply the negation equivalency

$$
LATEXBLOCK1
$$

Translate the symbolic result to English

$$ p \wedge \sim q: \text{"A fruit is blue, and it is a banana"} $$

Answer:

• A fruit is not blue, or it is not a banana
• A fruit is not blue, and it is a banana
• A fruit is blue, and it is not a banana
• A fruit is not blue, and it is not a banana
• If it is a banana, then a fruit is not blue
• If a fruit is not blue, then it is a banana
• A fruit is blue, and it is a banana (Correct answer)
• If it is not a banana, then a fruit is blue