Is ((~p ∧ q) ∧ (q ∧ r)) ∧ ~q a tautology, a contradiction, or neither a tautology nor a contradiction?
To find the answer, first complete the truth table below.
Which of the following answers the question?
The truth table shows that ((~p ∧ q) ∧ (q ∧ r)) ∧ ~q is true for every value of p, q, and r, and so it is a tautology.
The truth table shows that ((~p ∧ q) ∧ (q ∧ r)) ∧ ~q can be both true and false, depending on the values of p, q, and r, which proves that it is a contradiction.
The truth table shows that ((~p ∧ q) ∧ (q ∧ r)) ∧ ~q is false for every value of p, q, and r, and so it is a contradiction.
The truth table shows that ((~p ∧ q) ∧ (q ∧ r)) ∧ ~q can be both true and false, depending on the values of p, q, and r, which proves that it is neither a tautology nor a contradiction.
