Williams hires new faculty if either Smith increases enrollment or Amherst does not raise tuition, but Tulane reduces class size only if neither Rice expands course offerings nor Baylor offers new scholarships.
A) [W ⊃ ∼(S ∨ A)] ∨ [T ⊃ ∼(R ∨ B)]
B) [T ⊃ ∼(R ∨ B)] ⊃ [(S ∨ ∼A) ⊃ W]
C) [W ⊃ (S ∨ ∼A)] • [∼(R ∨ B) ⊃ T]
D) [(S ∨ ∼A) ⊃ W] • [T ⊃ ∼(R ∨ B)]
E) [(S ∨ ∼A) ⊃ W] • [T ⊃ (∼R ∨ ∼B)]

Question

Quizplus · Accepted Answer

The statement "Williams hires new faculty if either Smith increases enrollment or Amherst does not raise tuition" can be written as (S ∨ ∼A) ⊃ W using the contrapositive form of material implication.

The statement "Tulane reduces class size only if neither Rice expands course offerings nor Baylor offers new scholarships" can be written as ∼(R ∨ B) ⊃ T using the contrapositive form of material implication.

Combining these two statements using the logical operator "and" (&), we get:

(S ∨ ∼A) ⊃ W & ∼(R ∨ B) ⊃ T

Simplifying this statement, we get:

[(S ∨ ∼A) ⊃ W] • [T ⊃ ∼(R ∨ B)]

which matches with option D. Therefore, the correct answer is D.

Williams Hires New Faculty If Either Smith Increases Enrollment or Amherst