Which of the following has no solution? x ≤ 1 and x x < 1 and x x ≤ 1 or x

Question

Which of the following has no solution?

x ≤ 1 and x ≥ 1
x < 1 and x
x ≤ 1 or x ≥ 1

Answer 1

That would be the second option.

There is no number which is less than 1 and greater than 1.

Answer 2

x < 1 and x > 1

Explanation:

x and x

'And ' means the intersection of two inequalities

In both inequalities , we have 1 in common . So solution is 1

x and x

In both inequalities , there is no number in common because we have x<1 and x>1. there is no intersection for both inequalities. So, No solution.

x ≤ 1 or x ≥ 1

For 'or', the solution is the combination of both inequalities. So there is a solution.