Question

Which of the following has a solution set of {x | x = 0}?
(x + 1 < -1) ∩ (x + 1 < 1)

(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)

(x + 1 < 1) ∩ (x + 1 > 1)​

Answer 1

Step-by-step 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 | x = 0}

Answer 2

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