Which of the following has a solution set of x = 0? (x + 1 < -1) ∩ (x + 1 < 1) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) (x + 1 < 1) ∩ (x + 1 > 1)​

Question

Which of the following has a solution set of x ?

(x + 1 < -1) ∩ (x + 1 < 1)

(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)

(x + 1 < 1) ∩ (x + 1 > 1)​

Answer 1

Let's check one by one

#1

`\\ \sf\longmapsto x+1<-1\implies x<-2`

`\\ \sf\longmapsto x+1<1\implies x<0`

• Rejected

#2

`\\ \sf\longmapsto x+1\leqslant 1\implies x\leqslant 0`

`\\ \sf\longmapsto x+1\geqslant 1\implies x\geqslant 0`

Option B is correct

Answer 2

Explanation:

Middle option.

(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)

If you work both sides separately you get

(x ≤ 0) ∩ (x ≥ 0)

which reduces nicely to

x = 0