National's improving efficiency or Enterprise's reorganizing is a sufficient and necessary condition for Thrifty's laying off workers, provided that Avis buys new cars.
A) (N ∨ E) ≡ (A ⊃ T)
B) A ⊃ [(N ∨ E) ≡ T]
C) [(N ∨ E) ≡ T] ⊃ A
D) A ⊃ [(N ⊃ E) • (E ⊃ N)]
E) A ≡ [(N ∨ E) ⊃ T]

Question

Quizplus · Accepted Answer

The statement can be broken down into three parts: 
1) National's improving efficiency or Enterprise's reorganizing 
2) Avis buys new cars 
3) Thrifty lays off workers

According to the statement, 1) is a sufficient and necessary condition for 3) if 2) is true.

Choice B represents this relationship correctly. It states that if Avis buys new cars (A), then (N ∨ E) is equivalent to T. This means that if National improves efficiency or Enterprise reorganizes (N ∨ E), that is both sufficient and necessary for Thrifty to lay off workers (T), given that Avis buys new cars.

The other choices are incorrect: 
- Choice A has the correct sufficient condition (N ∨ E) but lacks the necessary condition A ⊃ T. 
- Choice C reverses the relationship, stating that (N ∨ E) ≡ T leads to A, which does not make logical sense based on the original statement. 
- Choice D introduces an additional requirement that (N ⊃ E) • (E ⊃ N), which is not stated in the original statement. 
- Choice E does not accurately reflect the conditional relationship between the variables.

National's Improving Efficiency or Enterprise's Reorganizing Is a Sufficient and Necessary