The Boolean expression p- q - q - - p - q is equivalent to

Consider, (p∧∼ q)∨ q∨ (∼ p∧ q) ≡ [(p∧∼ q )∨ q]∨ (∼ p ∧ q) . . .(Associtive Property) ≡ [(p∨ q)∧(∼ q ∨ q)]∨ (∼ p∧ q) . . .(Distributive Property) ≡ [(p∨ ...

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

Byju's Answer

Standard XI

Mathematics

Compound Statement

The Boolean e...

Question

The Boolean expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to

\sim p \land q

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

p \land q

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

p \lor q

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

p \lor \sim q

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

Open in App

Solution

The correct option is C $p \lor q$
Consider,
$(p \land \sim q) \lor q \lor (\sim p \land q) \equiv [(p \land \sim q) \lor q] \lor (\sim p \land q) . . . (A s s o c i t i v e P r o p e r t y) \equiv [(p \lor q) \land (\sim q \lor q)] \lor (\sim p \land q) . . . (D i s t r i b u t i v e P r o p e r t y) \equiv [(p \lor q) \land t] \lor (\sim p \land q) \equiv (p \lor q) \lor (\sim p \land q) . . . (∵ p \land t \equiv p) \equiv (p \lor q \lor \sim p) \land (p \lor q \lor q) \equiv (q \lor t) \land (p \lor q) \equiv t \land (p \lor q) \equiv p \lor q$

Suggest Corrections

Similar questions

Q. The Boolean expression

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

is equivalent to :

Q. The Boolean expression

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

is equivalent to

Q. The Boolean expression

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

is equivalent to

Q. The Boolean expression

(p \land q) \Rightarrow ((r \land q) \land p)

is equivalent to

Q. The Boolean expression

\sim (p \Rightarrow (\sim q))

is equivalent to :

Join BYJU'S Learning Program

The Boolean expression (p∧∼q)∨q∨(∼p∧q) is equivalent to

The Boolean expression $(p \land \sim q) \lor q \lor (\sim p \land q)$ is equivalent to