Question

The Boolean expression ~(p ⇒ (~q)) is equivalent to:
1. p ∧ q
2. q ⇒ ~p
3. p ∨ q
4. (~p) ⇒ q

Answer 1

Correct Answer - Option 1 : p ∧ q

From question, the Boolean expression given is:

~(p ⇒ (~q))

The truth table for the above expression is given below:

p	q	~q	P ⇒ (~q)	~(p ⇒ (~q))
T	T	F	F	T
T	F	T	T	F
F	T	F	T	F
F	F	T	T	F

 

Now, we need to consider the options:

Option (a) p ∧ q:

p	q	P ∧ q
T	T	T
T	F	F
F	T	F
F	F	F

 

Option (b) q ⇒ ~p:

p	q	~p	q ⇒ ~p
T	T	F	F
T	F	F	F
F	T	T	T
F	F	T	T

 

Option (c) p ∨ q:

p	q	P ∨ q
T	T	T
T	F	T
F	T	T
F	F	F

 

Option (d) (~p) ⇒ q:

p	q	~p	(~p) ⇒ q
T	T	F	T
T	F	F	T
F	T	T	T
F	F	T	F

 

On comparing the truth values of expression and truth values in options. The truth values in option is same and option (a) is the correct answer.