Which of the following has no solution?
{x | x < 0} and {x | x > 0}
{x | x ≤ 0} and {x | x ≥ 0}
{x | x ≤ 0} or {x | x ≥ 0}

The first one.
This statement is saying that x is less than zero and greater than zero at the same time. This is not possible. A number cannot be both negative and positive.
It's not the second one because this one includes equal to zero. It can be lass than or equal to zero and greater that or equal to zero because it can be ZERO.
It's not the third because this one is an OR statement. It can be less than or equal to zero OR greater than or equal to zero.
I hope you understand