Assertion (A): -8 < -5, 8 > -5, -8 < 5 and 8 > 5.
⇒ 8 > 5, -8 < 5, 8 > -5 and -8 < -5.
Reason (R): On changing the signs of both the sides of an inequation, the sign of inequality reverses.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Answer
First, let us check the inequalities given in the Assertion.
-8 < -5 (since |-8| > |-5|), 8 > -5 (positive > negative), -8 < 5 (negative < positive) and 8 > 5. All four are true.
Now changing the signs of both sides of each inequality reverses the sign of inequality:
-8 < -5 becomes 8 > 5; 8 > -5 becomes -8 < 5; -8 < 5 becomes 8 > -5; and 8 > 5 becomes -8 < -5.
These are exactly the four results stated after the ⇒ in the Assertion, so Assertion A is true.
The Reason states that on changing the signs of both sides of an inequation, the sign of inequality reverses. This is a correct property of inequalities (for example, 5 < 7 ⇒ -5 > -7), so Reason R is also true and it correctly explains the Assertion.
Thus, both A and R are true.
Hence, option 3 is the correct option.