Introduction to Logic
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Exercise 3.5 - Propositional Consistency

In each of the following cases, determine whether the given individual sentence is consistent with the given set of sentences.

a. {p ∨ q, p ∨ ¬q, ¬p ∨ q} and (¬p ∨ ¬q)
b. {p ⇒ r, q ⇒ r, p ∨ q} and r
c. {p ⇒ r, q ⇒ r, p ∨ q} and ¬r
d. {p ⇒ q ∨ r, q ⇒ r} and p ∧ q
e. {p ⇒ q ∨ r, q ⇒ r} and q ∧ r