Exam 6: Propositional Logic

Statement 3D Given the following statement: (M ⊃ ∼ E) ∨ (R ⊃ E) -Statement 3D is:

Travelers and Farmers cut costs given that Safeco opens new offices, but Metropolitan restructures if and only if either Nationwide expands coverage or Conseco reduces premiums.

If Williams increases enrollment, then not both Fordham and Georgetown expand course offerings.

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

Given the argument: P ∨ J / ∼(J • ∼ P) // J ≡ ∼ P This argument is:

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

S ? ?M $\frac{\mathrm{S}}{\sim \mathrm{M}}$

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C These statements are:

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:

(?W ? L) • (N ? ?R) $\frac { \mathrm { N } \vee \sim \mathrm { W } } { \mathrm { L } \vee \sim \mathrm { R } }$

Given the argument: (K • ∼ C) ⊃ ∼(P • R) / J ⊃ (K • P) / A ⊃ (P • R) // (A • J) ⊃ C This argument is:

Q ? ?S $\frac { S } { Q }$

Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.

?N ? W $\frac { \sim \mathrm { W } } { \sim \mathrm { N } }$

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

Statement 1C Given the following statement: (H ∨ ∼ K) ≡ (K ⊃ H) -Statement 1C is:

?S ? ?F $\frac { F } { S }$

S ? ?C $\frac{\sim \mathrm{C}}{\mathrm{S}}$

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G This argument is:

Toyota's closing a factory implies that Fiat improves mileage, given that both Chrysler and Nissan do not increase sales.