Q.

The Boolean expression ∼ (p ⇒ (∼ q)) is equivalent to


see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

(∼ p) ⇒ q

b

p ∨ q

c

q ⇒ ∼ p 

d

p ∧ q 

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Here, The given Boolean expression is ∼ (p ⇒ (∼ q)) .
p ⇒ (∼ q) is interpreted as (∼ p∨ ∼ q)
Now, ∼ (p ⇒ (∼ q)) can be written as ∼ (∼ p∨ ∼ q)
∼ (∼ p∨ ∼ q) can be interpreted as ∼ (∼ p) ∧ ∼ (∼ q)
By applying double complement law we can write
∼ (∼ p) ∧ ∼ (∼ q) is equivalent to p ∧ q
Thus, the given Boolean expression ∼ (p ⇒ (∼ q)) is equivalent to p ∧ q .

Hence, option (4) is correct for this question.
 
Watch 3-min video & get full concept clarity
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon