Question

x ∈ W, x ≥ −3 and x < 5. 

Statement (1): There will be no solution for the given inequations.

Statement (2): The real the given inequations is:

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Reason

x ≥ −3

Solution set of x = {−3, −2, −1, 0, 1, 2, ..........} ..... (1)

And, x < 5

Solution set of x = {.........., 1, 2, 3, 4} ..... (2)

From (1) and (2), we get

Solution set = {−3, −2, −1, 0, 1, 2, 3, 4}

So, statement 1 is false.

The real number line for the given inequations is:

So, statement 2 is true.