Question

What is the solution set of x ∩ x ?

all numbers except -3 and 5

the numbers between -3 and 5

the empty set

all real numbers

Answer 1

The answer will be empty set

Answer 2

The solution set of x < -3 ∩ x is:

The empty set

Explanation:

The first set is:

x < -3

This means that the solution of this set is: (-∞,-3)

and the second set is:

x > 5

This means that the solution set is: (5,∞)

Now, we know that intersection set contains the element that are common to both the set, i.e. it is a solution of first as well as second place.

Since, (-∞,-3)∩(5,∞)=∅

There no element which is common to both the set.

Hence, the answer is:

The empty set