Which of the following has no solution? \[ \{x \mid x \leq 0\} \text { and }[x \mid x \geq 0\} \] \( \{x \mid x<0\} \) and \( \{x \mid x>0\} \) \( [x \mid x \leq 0\} \) or \( [x \mid x \geq 0\} \)

In the case of \( \{x \mid x < 0\} \) and \( \{x \mid x > 0\} \), there is no solution because these two sets do not overlap at all. The first set includes all negative numbers, while the second set encompasses all positive numbers, leaving no possible values for \( x \) that would satisfy both conditions simultaneously. Similarly, when dealing with intervals like \( [x \mid x \leq 0\} \) or \( [x \mid x \geq 0\} \), while the second part does allow for zero, the 'or' condition allows for solutions that may be valid in one interval but not in the other. The important takeaway here is to always double-check the range of numbers you're working with to avoid confusion!