UGC-NET | UGC NET CS 2016 July – III | Question 70

Consider the statement, “Either – 2 ≤ x ≤ – 1 or 1 ≤ x ≤2”.
The negation of this statement is
(A) x < – 2 or 2 < x or – 1 < x < 1
(B) x < – 2 or 2 < x
(C) – 1 < x < 1
(D) x ≤ – 2 or 2 < x or – 1 < x < 1

Answer: (A)

Explanation: “Either – 2 ≤ x ≤ – 1 or 1 ≤ x ≤2”.
i.e. Eiter x ≥ -2 or x ≤ -1 or 1 ≤ x or x ≤ 2”
We have to find negation of above statement:
Negation of x ≥ -2 is x < 2. Negation of x ≤ -1 is x > -1.
Negation of 1 ≤ x is x < 1 Negation of x ≤ 2 is x > 2.
i.e. x < – 2 or 2 < x or – 1 < x < 1. So, option (A) is correct.

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