Question

1. For each of the following propositions construct a truth table and indicate whether it is a tautology (i.e., it’s always true), a contradiction (it’s never true), or a contingency (its truth depends on the truth of the variables). Also specify whether it is a logical equivalence or not. Note: There should be a column for every operator. There should be three columns to show work for a biconditional.

a) (P Λ ¬Q) ⇔ ¬(P ⇒ Q)

b) (¬? V¬?) ⇔ ¬(P Λ Q)

c) (P V Q) Λ ( ¬(? Λ Q) Λ (¬?))

d) (P ⇒ (Q Λ R)) ⇔ ((P ⇒ Q) Λ (Q ⇒ R))

e) (P ⇒ (Q ⇒ R)) ⇔ ((P ⇒ Q) ⇒ R) f) ((P V R) ⇒ (Q V S)) ⇒ ((P⇒ Q) Λ (R ⨁ S))

with biconditional and There should be a column for every operator

Answer 1