The logically equivalent statements are a. (p∨∼q)
Let's analyze the logical equivalence of each statement:
Given
∼(p∨q), which is the negation of (p∨q).
a. (p∨∼q)
This is logically equivalent. De Morgan's Law states that ∼(p∨q) is equivalent to (∼p∧∼q).
b. (∼p∨q)
This is not logically equivalent. It is the negation of (p∨∼q), not ∼(p∨q).
c. (p∧q)
This is not logically equivalent. It is the negation of (p∨q), not ∼(p∨q).
d. (p∨q)
This is not logically equivalent. It is the opposite of ∼(p∨q).
e. (p∧∼q)
This is not logically equivalent. It is the negation of (p∨q), not ∼(p∨q).
f. (p∧q)
This is not logically equivalent. It is the negation of (p∨q), not ∼(p∨q).
Therefore, the logically equivalent statements are:
a. (p∨∼q)