JAMIA 2022 — Mathematics PYQ

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Question

JAMIA 2022 — Mathematics PYQ

JAMIA | Mathematics | 2022

(p ^ ~ q) ^ (~ p ^ q)

Choose the correct answer:

Explanation

Step 1: Analyze the Expression

The expression consists of two parts connected by an "AND" ( $\land$ ) operator:

Part 1: $(p \land \neg q)$
Part 2: $(\neg p \land q)$

Step 2: Use Associative and Commutative Laws

Since all the operators in the expression are the same (all are $\land$ ), we can remove the parentheses and rearrange the terms in any order:

(p \land \neg q) \land (\neg p \land q) = p \land \neg q \land \neg p \land q

Rearrange to group the $p$ terms together and the $q$ terms together:

= (p \land \neg p) \land (q \land \neg q)

Step 3: Apply the Law of Contradiction

The Law of Contradiction states that a statement and its negation cannot both be true at the same time:

$p \land \neg p = F$ (False/Contradiction)
$q \land \neg q = F$ (False/Contradiction)

Substituting these back into our expression:

= F \land F

Step 4: Final Result

In logic, "False AND False" is always False:

F \land F = F

Final Answer

The expression is a Contradiction (always False).

(p \land \neg q) \land (\neg p \land q) \equiv F