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UGC-NET | UGC NET CS 2016 Aug – II | Question 1
  • Last Updated : 10 Apr, 2018

The Boolean function [~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)] is equal to the Boolean function:
(A) q
(B) p ∧ r
(C) p ∨ q
(D) p


Answer: (D)

Explanation:
We have Boolean function:
[~(~p ∧ q) ∧ ~( ~p ∧ ~q)] ∨ (p ∧ r)]
= [(p ∨ ~q) ∧ (p ∨ q ) ∨ (p ∧ r)]
= [p ∨ (p ∧ q) ∨ (p ∧ ~q) ∨(p ∧ r)]
= p[1 ∨ q ∨ ~q ∨ r]
= p
So, option (D) is correct.


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