Inequality rules and operations – UGC NET Question

Statements A, B and C summarise fundamental rules about inequalities. A is true because “greater than” is transitive. B is correct since multiplying by a positive constant preserves the order. C is also correct because multiplying by a negative constant reverses the direction of an inequality. D is false; knowing a > b and c > d does not ensure any fixed relation between a − c and b − d. E is false since squaring can change the order when negative numbers are involved, so the correct set of statements is A, B and C only.

Option A:
Option A is incomplete as it lists only A and B and omits C, so it does not mention how multiplying by a negative constant affects the inequality, which is crucial in many exam problems. This makes the option insufficient.

Option B:
Option B is also incomplete because it includes A and C only and leaves out B, thereby ignoring the important case of multiplication by positive numbers, which must also be understood.

Option C:
Option C is incomplete since it contains only B and C and omits A, losing the basic transitivity property that is often used to chain inequalities. Without A, the rule set is not fully represented.

Option D:
Option D is correct as it gathers all three true rules and explicitly excludes D and E, both of which overgeneralise operations on inequalities. It matches the standard algebraic handling of inequalities in NET-level aptitude questions.