UGC NET CSE | June 2016 | Part 3 | Question: 70

Question

Consider the statement 

"Either $-2 \leq x \leq -1 \text{ or } 1 \leq x \leq 2$"

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 $\leq$ -2 or 2 $\leq$ x or  -1<x<1

Answer 1

Hope the correct question is "Either -2<=x<=-1  or 1<=x<=2 ".

Then answer will be (1)

     ========-2======-1=======1=====2========  

Imagine this is a number line.

x is indicated by red segments

negation of x is indicated by blue segments which is x<-2 or 2<x  or -1<x<1

Comments

What if "either" is removed from question?

---

But If the given question is right I think (2) is the right answer

Answer 2

Either -2<=x<=01 or 1<=x<=2 "

~(Either -2<=x<=01 or 1<=x<=2 ")

(-2> x OR x> 1) AND ( 1> x OR x> 2)