JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.
A) J ≡ ∼(D • S)
B) J ⊃ (∼D • ∼S)
C) J ≡ (∼D • ∼S)
D) ∼(D ∨ S) ⊃ J
E) J ∨ (∼D • ∼S)

Question

Quizplus · Accepted Answer

The statement "JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes" means that for JetBlue to buy planes, two conditions must be met: (1) Delta is not advertising a sale, and (2) Southwest is not expanding routes.

This is represented by the logical statement J ≡ (∼D • ∼S), where J stands for JetBlue buys planes, ∼D stands for Delta not advertising a sale, and ∼S stands for Southwest not expanding routes.

Option A is incorrect as it represents the logical statement J ≡ ∼(D • S), which means that JetBlue buys planes only if Delta and Southwest do not advertise sales or expand routes, which is not the same as the original statement.

Option B is incorrect as it represents the logical statement J ⊃ (∼D • ∼S), which means that if JetBlue buys planes, then both Delta does not advertise a sale and Southwest does not expand routes. This statement does not capture the "if and only if" condition in the original statement.

Option D is incorrect as it represents the logical statement ∼(D ∨ S) ⊃ J, which means that if neither Delta nor Southwest are advertising sales or expanding routes, then JetBlue buys planes. This statement does not capture the "if and only if" condition in the original statement.

Option E is incorrect as it represents the logical statement J ∨ (∼D • ∼S), which means that either JetBlue buys planes or both Delta does not advertise a sale and Southwest does not expand routes. This statement does not capture the "if and only if" condition in the original statement.

JetBlue Buys Planes If and Only If Both Delta Does