Answer

Correct Option: (i) $P$: True, $Q$: False

Explanation

Given statement: $(\sim P \leftrightarrow Q) \land \sim Q$

For the conjunction to be true, both parts must be true:

1. $\sim Q$ is true $\implies Q = \text{False}$
2. $(\sim P \leftrightarrow Q)$ must be true with $Q = \text{False}$

Biconditional truth condition

$A \leftrightarrow B$ is true iff $A$ and $B$ have same truth value.

So with $Q = \text{False}$:
$$\sim P \leftrightarrow Q = \text{True} \implies \sim P = Q = \text{False} \implies P = \text{True}$$

Verification via Truth Table

$P$	$Q$	$\sim P$	$\sim P \leftrightarrow Q$	$\sim Q$	$(\sim P \leftrightarrow Q) \land \sim Q$
T	T	F	F	F	F
T	F	F	T	T	T
F	T	T	T	F	F
F	F	T	F	T	F

Only row $P=T, Q=F$ yields true.

Final Answer

The statement is true exactly when $P$ is True and $Q$ is False, i.e., option (i).