Answer to Question #284367 in Discrete Mathematics for Jacy

Question

Use the truth tables method to determine whether (¬p ∨ q) ∧ (q → ¬r ∧ ¬p) ∧ (p ∧ r) is

satisfiable.

Answer 1

Solution:

Δ = {(¬p ∨ q) ∧ (q → ¬r ∧ ¬p) ∧ (p ∧ r)}

If any sentence evaluates to 0, then Δ as a whole is not satisfied by the truth assignment. If a satisfying truth assignment is found, then Δ is determined to be satisfiable. If no satisfying truth assignment is found, then Δ is unsatisfiable.

In this question, every row ends with Δ not satisfied. So the truth table method concludes that Δ is unsatisfiable.