GATE CSE 2015 Set 1 | Question: 1‏4

Question

Which one of the following is NOT equivalent to $p ↔ q$?

• A. $(\neg p ∨ q) ∧ (p ∨ \neg q)$
• B. $(\neg p ∨ q) ∧ (q → p)$
• C. $(\neg p ∧ q) ∨ ( p ∧ \neg q)$
• D. $(\neg p ∧ \neg q) ∨ (p ∧ q)$

Answer 1

$(p \iff  q)$

$= (p\to q)\wedge (q\to p)$

$= (\neg p\vee q)\wedge (q\to p)$   (Option B)    As$(p\to q = \neg p\vee q )$

$=(\neg p\vee q)\wedge  (\neg q\vee p)$ (Option A)

$=(\neg p\wedge \neg q)\vee (p\wedge q)$ (Option D)

So, answer C is not equivanet to $p \iff q$ and is the answer.

Comments

please check option C is not matching its Option D

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Option C (¬p ∧ q ) ∨ (p ∧ ¬q ) is correct, as it is xor. Option D is xnor and thus same as equivalent. If we put both p and q true or both false, D is true. C is NOT so C must be the answer.

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Fixed now

Answer 2

Option A, B, D comes out to be P ↔ Q.

Option C is P xor Q.

Answer : C

Answer 3

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