Question

The propositional variables f, h, and p represent the propositions:___________f: The student got an A on the final.h: The student turned in all the homework.p: The student is on academic probationSelect the logical expression that represents the statement: "The student is not on academic probation and the student got an A on the final or turned in all the homework."

Answer 1

The options are:

`(A)\\eg p \land (f \lor h)\\(B)(\\eg p \land f) \lor h\\(C)\\eg p \land f \land h\\(D)\\eg( p \land f) \lor h`

Answer:

`(B)(\\eg p \land f) \lor h`

Step-by-step explanation:

Given the propositional variables:

• f: The student got an A on the final.
• h: The student turned in all the homework.
• p: The student is on academic probation

The negation of p,
`\\eg p=$The student is not on academic probation`

• A AND B (Logical conjunction) is written as:
  `A \land B`
• A OR B (Logical disjunction) is written as:
  `A \lor B`

Therefore, the logical expression for the statement:

"The student is not on academic probation and the student got an A on the final " is:
`\\eg p \land f`

Therefore, the logical expression for the given statement

"The student is not on academic probation and the student got an A on the final or turned in all the homework."

is:
`(\\eg p \land f) \lor h`

The correct option is B.