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GATE | GATE-CS-2014-(Set-3) | Question 65

  • Difficulty Level : Easy
  • Last Updated : 28 Jun, 2021

Consider the following statements:

  P: Good mobile phones are not cheap
  Q: Cheap mobile phones are not good

  L: P implies Q
  M: Q implies P
  N: P is equivalent to Q 

Which one of the following about L, M, and N is CORRECT?

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(A) Only L is TRUE.
(B) Only M is TRUE.
(C) Only N is TRUE.
(D) L, M and N are TRUE


Answer: (D)

Explanation:

Let a and b be two proposition
a: Good Mobile phones.
b: Cheap Mobile Phones.

P and Q can be written in logic as
P: a-->~b
Q: b-->~a.

Truth Table
a   b   ~a  ~b   P   Q
T   T   F    F   F   F
T   F   F    T   T   T
F   T   T    F   T   T
F   F   T    T   T   T

it clearly shows P and Q are equivalent.
so option D is Correct


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