Exam 6: Propositional Logic

(?N ? R) • (F ? ?G) $\frac{F \vee \sim N}{R \vee \sim G}$

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.

Given the pair of statements: ∼ (S ⊃ Q) and ∼ Q • S These statements are:

Statement 3A Given the following statement: [∼ H ∨ (E • D)] ≡ [(H • ∼ E) ∨ (H • ∼ D)] -Statement 3A is:

Given the argument: S ≡ (N ∨ H) / S ∨ ∼N // S ⊃ H This argument is:

Given the statements: (E ∨ P) ⊃ H / ∼ N ⊃ (P • E) / N ⊃ ∼ H / E ≡ ∼ P These statements are:

Statement 3I Given the following statement: [K • (P ∨ ∼ R)] • [K ⊃ (R • ∼ P)] -Statement 3I is:

Amherst reduces class size, and either Williams increases enrollment or Smith raises tuition.

United lowers fares if and only if both JetBlue buys planes and Delta advertises a sale, provided that American hires pilots.

Rice hires new faculty only if neither Duke nor Tulane increases student aid.

(?C ? ?J) • (P ? L) $\frac { \mathrm { J } V \sim \mathrm { L } } { \mathrm { C } \vee \sim \mathrm { P } }$

?E ? ?H $\frac { \sim \mathrm { H } } { \sim \mathrm { E } }$

Not both Playboy changes its image and Maxim changes its cover given that Glamour hires models.

Budget lowers rates unless Hertz and Thrifty do not overhaul operations.

Statement 2H Given the following statement: [N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)] -The truth table for Statement 2H has how many lines?

Suppose an indirect truth table is constructed for a series of statements, and the truth table requires more than one line. If a contradiction is reached on the first line, then:

Proposition 2F Given the following proposition: [(X ⊃ ∼ Y) • ∼ (X ∨ ∼ B)] ⊃ [∼ (B ⊃ ∼ Y) ≡ (A • ∼ Y)] -In Proposition 2F, the main operator is a:

Given the statements: J ⊃ B / B ⊃ (N ∨ C) / N ⊃ C / J • ∼C These statements are:

Tulane increasing enrollment is a necessary condition for Duke's reducing class size if and only if Fordham's raising tuition is a sufficient condition for Georgetown's expanding course offerings.

F ? ?K $\frac { \sim \mathrm { N } \supset \mathrm { F } } { \sim \mathrm { N } \supset \sim \mathrm { K } }$