If p and q are two statements, then which of the following statements is not equivalent to p⇔p⇒q?

Question

MARKS Content Team · Accepted Answer

Correct answer: (D) ~q⇒p∧p⇒~q. p q p⇒q p⇔p⇒q T T T T T F F F F T T F F F T F ⇒p⇔p⇒q≡p∧q⇒A is true Now, q⇔q⇒p≡p∧q≡p∧q ⇒q⇒p⇒q≡p∧q⇒C is true Now, common between p⇔q & p∨q is p∧q⇒p⇔q∧p∨q≡p∧q ⇒B is correct Now, ~q⇒p∧p⇒~q≡q∨p∧~p∨~q = Only p or only q≡~p⇔q

$p$	$q$	$p \Rightarrow q$	$p \Leftrightarrow (p \Rightarrow q)$
T	T	T	T
T	F	F	F
F	T	T	F
F	F	T	F

If $p$ and $q$ are two statements, then which of the following statements is not equivalent to $p \Leftrightarrow (p \Rightarrow q)$ ?

Solution

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