Question

What is the solution set of{xlx < 2) U{xIx > 2)?

Answer 1

The solution set is (-∞, 2) U (2, ∞).

Step-by-step explanation:

The solution set of the given expression {xlx < 2) U{xIx > 2) can be found by considering each inequality separately.

For x < 2, the solution set includes all values less than 2.

• If we take x = 1, the inequality x < 2 is satisfied.
• If we take x = 2, the inequality x < 2 is not satisfied since it is asking for values strictly less than 2, not inclusive.

For x > 2, the solution set includes all values greater than 2.

• If we take x = 3, the inequality x > 2 is satisfied.
• If we take x = 2, the inequality x > 2 is not satisfied since it is asking for values strictly greater than 2, not inclusive.

Combining the solution sets for both inequalities, we get all values less than 2 U all values greater than 2, which is represented as (-∞, 2) U (2, ∞).