What is the solution set of {x | x < -3} ∩ {x | x > 5}?

Solution:

The intersection of two given sets is the set that contains all the elements that are common to both sets.

The symbol for the intersection of sets is "∩''. For any two sets A and B, the intersection, A ∩ B (read as A intersection B) lists all the elements that are present in both sets, the common elements of A and B.

The best way to find the answer for such questions is by using a number line.

The blue zone indicates the first part of the set and the orange zone indicates the second part.

In between ∩ means the terms which are similar in both the parts

As you can see that no colour overlaps one another

It is an empty set.

Therefore, the solution set is an empty set.

What is the solution set of {x | x < -3} ∩ {x | x > 5}?

Summary:

The solution set of {x | x < -3} ∩ {x | x > 5} is an empty set.