The statement (~P<->Q)∧~Q is true when?a.P: False Q: Falseb.P: True Q: Falsec.P: False Q: Trued.P: True Q: True

Let's break down the statement and evaluate each option:

The statement is (~P<->Q)∧~Q. This can be read as "not P if and only if Q AND not Q".

a. P: False Q: False The statement becomes (~False <-> False) ∧ ~False which simplifies to (True <-> False) ∧ True. The first part of the statement (True <-> False) is False, so the whole statement becomes False ∧ True, which is False.

b. P: True Q: False The statement becomes (~True <-> False) ∧ ~False which simplifies to (False <-> False) ∧ True. The first part of the statement (False <-> False) is True, so the whole statement becomes True ∧ True, which is True.

c. P: False Q: True The statement becomes (~False <-> True) ∧ ~True which simplifies to (True <-> True) ∧ False. The first part of the statement (True <-> True) is True, so the whole statement becomes True ∧ False, which is False.

d. P: True Q: True The statement becomes (~True <-> True) ∧ ~True which simplifies to (False <-> True) ∧ False. The first part of the statement (False <-> True) is False, so the whole statement becomes False ∧ False, which is False.

So, the statement (~P<->Q)∧~Q is true when P is True and Q is False.