DISCRETE MATHS

Question

Consider the statement 

"Either −2≤x≤−1 or 1≤x≤2−2≤x≤−1 or 1≤x≤2"

The negation of this statement is 

1. x<-2 or 2<x  or -1<x<1
2. x<-2 or 2<x
3. -1<x<1
4. x ≤≤ -2 or 2 ≤≤ x or  -1<x<1

I THINK NONE OF THESE ????

Answer 1

Let, Statement A: -2 <= x <= -1

and Statement B : 1 <= x <= 2

Here we have to find negation (A OR B)

We know that negation (A OR B) = negation (A) AND negation (B)

Here negation (A) = x< -2 OR x > -1

and negation (B) = x<1 OR x>2

Hence negation(A) AND negation(B) = x< -2 OR x >2 OR -1 < x < 1

which is option 1.

Hence the 1st option will be the correct answer.