Exam 6: Propositional Logic

If deficit spending is halted, then interest rates will drop; but if inflation heats up, then interest rates will not drop. Accordingly, either deficit spending will not be halted or inflation will not heat up, since interest rates will either drop or not drop.

E ? ?T $\frac { \sim \mathrm { N } \supset \mathrm { E } } { \sim \mathrm { N } \supset \sim \mathrm { T } }$

Given the argument: Q ⊃ (C • N) / S ⊃ (C ∨ N) / Q ∨ S / N ⊃ K // K • C This argument is:

If eggs do not contain cholesterol, then they are healthy to eat. But eggs do contain cholesterol. Thus, eggs are not healthy to eat.

Given the pair of statements: G ⊃ (W • ∼ Q) and (W ∨ ∼ G) • ∼(Q • G) These statements are:

If Shape expands coverage, then neither Money hires new writers nor Forbes solicits new advertisers.

If our company reduces wages, then it will lose its labor force; but if it does not reduce wages, then it will go bankrupt. Thus, our company will either lose its labor force or go bankrupt, since it will either reduce wages or not reduce them.

American's hiring pilots is a sufficient condition for both Delta's advertising a sale and Southwest's expanding routes.

Proposition 2E Given the following proposition: [∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)] -Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.

Both Nissan lays off workers if Fiat improves mileage and Honda reduces inventory only if Mercedes introduces a new model.

Statement 2F Given the following statement: (Q ⊃ ∼ C) • (R ⊃ ∼ Q) -The truth table for Statement 2F has how many lines?

R $\frac{\mathrm{R} \supset \sim \mathrm{D}}{\sim \mathrm{D}}$

JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.

?S $\frac { \sim \mathrm { S } \supset \mathrm { F } } { \mathrm { F } }$

The dot operator is used to translate:

Given the statements: P ⊃ (A ⊃ M) / (D ∨ K) ⊃ (M ⊃ H) / (A • ∼ H) ∨ ∼ D / P • D These statements are:

Given the argument: A ⊃ ∼B / B ∨ A // ∼B ≡ A. This argument is:

If either Nationwide's running an ad or Progressive's paying a dividend implies that Allstate hires agents, then Safeco's opening new offices is a sufficient and necessary condition for Liberty's reducing premiums.

Given the argument: Q ⊃ (A ∨ M) / A ⊃ (W ∨ C) / M ⊃ (E ∨ C) / ∼(W ∨ E) // Q ⊃ C This argument is:

?F ? L $\frac{\mathrm{F}}{\sim \mathrm{L}}$