Question

Let A=\x:x R, |x|<1 B=\x:x R, |x-1| 1 and A B=R-D, then the set D is

• A. \x:1
• B. \x:1 x<2
• C. \x:x 2
• D. None of these

Hint:

Find complements by locating gaps on the number line.

Answer 1

The Correct Option is A

Step 1: A=(-1,1)
Step 2: |x-1|\ge1 x\le0 or x\ge2 So, B=(-∞,0][2,∞)
Step 3: A B = (-∞,1)[2,∞)
Step 4: Missing set is D=(1,2]