Exam 6: Propositional Logic

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and a contradiction is derived on the first line, then:

If Redbook's hiring models implies that Cosmo changes its cover, then either Maxim becomes more risqué or Playboy deletes its centerfold.

Princess and Azmara improve gym facilities only if neither Carnival controls rowdiness nor Seabourn reduces fares.

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Statement 2E Given the following statement: (P ⊃ ∼ B) ∨ (B ⊃ ∼ L) -The truth table for Statement 2E has how many lines?

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

Proposition 1D Given the following proposition: ∼ (A • ∼ X) ≡ [A ⊃ (Y ∨ ∼ B)] -Given that A and B are true and X and Y are false, determine the truth value of Proposition 1D.

If computers can play chess, then they can think. But computers cannot think. Thus, computers cannot play chess.

Escaping between the horns of a dilemma means:

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

Given the pair of statements: (A ∨ B) • (∼ A ∨ ∼ B) and (B • A) ∨ (∼ A • ∼ B). These statements are:

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.

Frontier's improving service is a necessary condition for either JetBlue's buying planes or United's lowering fares.

Frontier's improving service implies that not both JetBlue buys planes and Southwest expands routes.

Statement 3G Given the following statement: [A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)] -Statement 3G is:

Statement 2G Given the following statement: ∼ (B ∨ A) ≡ (∼ A ⊃ B) -Statement 2G is:

Given the argument: C ⊃ ∼ M / I ⊃ ∼ H / (N • I) ∨ (G • C) / H ∨ M // G • M This argument is:

Given the argument: (S ∨ B) ⊃ M / S ∨ ∼ Q / A ⊃ B / A ∨ Q // M This argument is:

Coors is smooth or both Beck's is subtle and Guinness is heavy.

Williams offers new scholarships if and only if either Amherst reduces class size or Smith does not hire new faculty.