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 probation
Write 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."
Compound logical statement:
Demonstrate your compound logical statement is equivalent to: (p→) ∨ (p→ℎ):
Demonstrate your compound logical statement is equivalent to: ¬((p ∨¬)∧(p∨¬ℎ)):

Answer 1

The logical expression that represents the statement is ¬p ∧ (f ∨ h). It is equivalent to (p → ¬h) ∨ (p → f).

Step-by-step explanation:

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' is:

¬p ∧ (f ∨ h)

To demonstrate that this logical expression is equivalent to (p → ¬h) ∨ (p → f), we can break it down into two parts:

Part 1: ¬p ∧ (f ∨ h) → (p → ¬h) ∨ (p → f)

We can assume the left side of the implication is true and show that the right side must also be true: If the student is not on academic probation and they got an A or turned in all the homework, then either if the student is on academic probation, they did not turn in all the homework (¬h), or if the student is on academic probation, they got an A (f).

Part 2: (p → ¬h) ∨ (p → f) → ¬p ∧ (f ∨ h)

We can assume the right side of the implication is true and show that the left side must also be true: If either if the student is on academic probation, they did not turn in all the homework (¬h), or if the student is on academic probation, they got an A (f), then the student is not on academic probation and they got an A or turned in all the homework.