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GATE | GATE CS 2008 | Question 33

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  • Difficulty Level : Basic
  • Last Updated : 11 Oct, 2021
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P and Q are two propositions. Which of the following logical expressions are equivalent? 

 

\"q29\"

 

(A)

All of I, II, III and IV
 

(B)

Only I, II and IV
 

(C)

Only I, II and III
 

(D)

Only I and II 
 


Answer: (C)

Explanation:

I and II are same by Demorgan’s law

The IIIrd can be simplified to I. 

\\newline \\equiv P \\wedge (Q \\vee \\neg Q)\\vee(\\neg P \\wedge \\neg Q) \\newline \\equiv P \\vee (\\neg P \\wedge \\neg Q) \\newline \\equiv (P \\vee \\neg P) \\wedge (P \\vee \\neg Q) = (P \\vee \\neg Q) since P\\vee \\neg P is true always 

 


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