A set would not normally have a solution. An equation or an inequality might.
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You simply call it "no solution".
That's called the "solution set".
Yes, empty set means null which is no solution.
An empty set is a set with no elements. It can be symbolized by {} or ø. The solution set for an equation that has no solution is also called an empty set.
Unsolvable equations have no solutions so the solution set would be [ ]. (empty set)