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 you pass this course, then you will graduate this semester.\

• if you graduate this semester, then you pass this course
• you dont pass this course, or you graduate this semester
• you pass this course, and you do not graduate this semester
• if you do not graduate this semester, then you dont pass this course
• if you dont pass this course, then you do not graduate this semester
• you dont pass this course, and you do not graduate this semester
• you dont pass this course, and you graduate this semester
• you pass this course, and you graduate this semester

Explanation:

Define the propositional variables

$$
LATEXBLOCK0
$$

Translate the conditional statement and its negation

$$
LATEXBLOCK1
$$

Translate the equivalent symbolic form back to English

$$ p \wedge \sim q: \text{"You pass this course, and you do not graduate this semester."} $$

Answer:

• If you graduate this semester, then you pass this course
• You don't pass this course, or you graduate this semester
• You pass this course, and you do not graduate this semester (Correct answer)
• If you do not graduate this semester, then you don't pass this course
• If you don't pass this course, then you do not graduate this semester
• You don't pass this course, and you do not graduate this semester
• You don't pass this course, and you graduate this semester
• You pass this course, and you graduate this semester