The logical statement - p - q - p - q is equivalent toA- PB- qC- - pD- - q

The correct option is D ∼ q∼(∼ p → q)∨(p ∧∼ q) = ∼(∼ (∼ p) ∨ q)∨(p ∧∼ q) (∵ p → q ≡∼ p ∨ q) = ∼( p ∨ q)∨(p ∧∼ q) = (∼ nbsp; p ∧ nbsp; ∼ q)∨(p ∧∼ q) =( ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Distributive Law

The logical s...

Question

The logical statement $\sim (\sim p \to q) \lor (p \land \sim q)$ is equivalent to

p

No worries! We‘ve got your back. Try BYJU‘S free classes today!

q

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sim p

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sim q

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\sim q$
$\sim (\sim p \to q) \lor (p \land \sim q)$
$=\sim (\sim (\sim p) \lor q) \lor (p \land \sim q) (∵ p \to q \equiv\sim p \lor q)$
$=\sim (p \lor q) \lor (p \land \sim q)$
$= (\sim p \land \sim q) \lor (p \land \sim q)$
$= (p \land \sim p) \lor \sim q$
$= F \lor \sim q$
$=\sim q$

Suggest Corrections

Similar questions

Q. The expression

\sim (p \lor q) \lor (\sim p \land q)

is logically equivalent to

Q. The statement

p \to (q \to p)

is logically equivalent to

Q. The logically equivalent proposition of

p \Leftrightarrow q

The statement $p \Rightarrow\sim q$ is equivalent to

Q. For any two statements

p

and

q,

the expression

\sim (p \lor q) \lor (\sim p \land q)

is logically equivalent to

Join BYJU'S Learning Program

The logical statement ∼(∼p→q)∨(p ∧∼q) is equivalent to

The correct option is D ∼q∼(∼p→q)∨(p ∧∼q) =∼(∼(∼p)∨q)∨(p ∧∼q) (∵p→q≡∼p∨q) =∼(p∨q)∨(p ∧∼q) =(∼p ∧∼q)∨(p ∧∼q) =(p ∧∼p)∨∼q =F ∨∼q =∼q

The logical statement $\sim (\sim p \to q) \lor (p \land \sim q)$ is equivalent to