Final answer:
The statement ￢(p ∧ q) ≡ ￢p ∧ ￢q is true.
Step-by-step explanation:
The statement ￢(p ∧ q) ≡ ￢p ∧ ￢q is true.
To prove this, we can use a truth table. First, we need to evaluate ￢(p ∧ q) and ￢p ∧ ￢q for all possible truth values of p and q.
Truth table for ￢(p ∧ q):
pq￢(p ∧ q)true true false true false true false true true false false true
Truth table for ￢p ∧ ￢q:
pq￢p￢q￢p ∧ ￢qtruetruefalsefalsefalsetruefalsefalsetruefalsefalsetruetruefalsefalsefalsefalsetruetruetrue
By comparing the truth tables, we can see that the two statements have the same truth values for all possible combinations of p and q. Therefore, the statement ￢(p ∧ q) ≡ ￢p ∧ ￢q is true.