# 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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