Question

PLEASE HELP..............

Which of the following has no solution?

x < 0 and {x I x > 0}
x ≤ 0 and x ≥ 0
x or x ​

Answer 1

x and {x I x > 0} has no solution

Explanation:

x cannot be less than zero AND more than zero at the same time, so the first inequality has no solution.

x < 0 and {x I x > 0}

Answer 2

A

Explanation:

Choice A has the two options:

`x<0 \text{ and } x>0`

In other words, x must be a number such that it is negative (left option) and positive (right option) at the same time.

There can't be such number (and 0 is not included in the answer choices since it is not less/more than or equal to). Thus, Choice A has no solution.

The keyword here is and. If instead of and it was or, then the choice does indeed have a solution.