Question

Complete the truth table for the given compound statement and then decide which statements within the given statement are logically equivalent. (p∨q)∨∼(p⇒q)

Options:
A) p ∧ q
B) ∼p ∨ ∼q
C) ∼p ∧ ∼q
D) p ∨ ∼q

Answer 1

The given compound statement is (p∨q)∨∼(p⇒q). The truth table shows that the statements (p∨q) and ∼(p⇒q) are equivalent when both p and q are true or when p is false and q is true.

Step-by-step explanation:

The given compound statement is (p∨q)∨∧(p⇒q). To complete the truth table, we need to consider all possible combinations of truth values for p and q. There are 4 possible combinations:

pq(p∨q)∧(p⇒q)TTTTTFTFFTTTFFFT

From the truth table, we can see that the statements (p∨q) and ∧(p⇒q) are equivalent when both p and q are true or when p is false and q is true.

Therefore, the correct answer is A) p ∧ q.