Question

Assertion (A): For the inequation $$-12 < 3 - 4x \leq 11,\ x \in \mathrm{N}$$, the solution set is {1, 2, 3, 4}.

Reason (R): The set of all those values of $$x$$ from the replacement set which satisfy the given inequation is called the solution set of the inequation.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Step 1 – Assertion: A is false. Solving the inequation gives $$-2 \leq x < \frac{15}{4}$$. Since $$x \in \mathrm{N}$$, the solution set is {1, 2, 3}, not {1, 2, 3, 4}.

Step 2 – Reason: R is true. It correctly defines the solution set as the values from the replacement set that satisfy the inequation.