Question

Assertion: `-8 1/2 < - 1/2 -4x <= 7 1/2, x ∈ l` gives x ∈ (−2, −1, 0}

Reason: The set from which the values of the variable involved in the equation are chosen, is called the replacement set.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is false but Reason (R) is true.

Explanation:

Given:

`-8 1/2 < - 1/2 -4x <= 7 1/2, x ∈ l`

`-17/2 < -1/2 - 4x <= 15/2`

`-16/2 < -4x <= 16/2`

−8 < −4x ≤ 8

Divide by −4:

2 > x ≥ −2

−2 ≤ x < 2

x ∈ {−2, −1, 0, 1}

But the assertion says:

x ∈ {−2, −1, 0}

Assertion (A) is false.

Reason (R) is true.