Question

Which of the following has no solution?

(x + 1 < -1) ∩ (x + 1 < 1)
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 < 1) ∩ (x + 1 > 1)

Answer 1

in first choice we have two sets

1st set: x+1 < -1

x< -2

2nd: x+1 <1
x < 0

so if there are solutions to first choice, there are numbers that are both less than -2 and less than 0. There are such numbers (-5, -6 .... )

Answer 2

in second choice

1st set :x+1 =< 1

x =< 0

2nd: x+1 >=1
x>=0

th solution to this one will be 0

so lets check 3rd choice

Answer 3

in third one we don't have solutions

x+1<1 -----> x<0
x+1>1 ------> x>0

so no soutions

Answer 4

so C

Answer 5

thank you:)

Answer 6

nope :)