Q.If $p \wedge q$ is false and $p \vee q$ is true, then ________ is not true.
A) $p \vee q$
B) $p \leftrightarrow q$
C) $\sim p \vee \sim q$
D) $q \vee \sim p$

Given $p \wedge q$ is False and $p \vee q$ is True. $p\wedge q$ False rules out both being True; $p \vee q$ True rules out both being False. So exactly one of $p,q$ is True and the other False — the two cases are ($p{=}T,q{=}F$) or ($p{=}F,q{=}T$).

Check each option in both cases:

• A) $p \vee q$: True in both cases (given) — always true, so not the answer.
• B) $p \leftrightarrow q$: Case 1, $T \leftrightarrow F = F$. Case 2, $F \leftrightarrow T = F$. False in BOTH cases — this is never true.
• C) $\sim p \vee \sim q$: Case 1, $F \vee T = T$. Case 2, $T \vee F = T$. Always true, so not the answer.
• D) $q \vee \sim p$: Case 1, $F \vee F = F$. Case 2, $T \vee T = T$. Sometimes true, sometimes false — not a clean 'never true' answer like B.

Only option B is False in every case consistent with the given data.

Deduce that $p,q$ must differ, then test each option against both possible assignments.

Picking D because it is false in one case, without checking it is also true in the other case — the correct answer must be false in ALL cases consistent with the given data.