Q196
ReasoningSyllogism & Logical Deduction
"Having four equal sides is a necessary condition for a quadrilateral to be a square, but it is not sufficient." This means:
- a.A quadrilateral cannot be square unless it has four equal sides, but having four equal sides doesn't guarantee a quadrilateral to be a square.
- b.No quadrilateral with four equal sides is a square.
- c.For a quadrilateral to be a square, all four sides cannot be equal.
- d.In Mathematics, equality of sides is unrelated to the condition for a quadrilateral to be a square.
Answer: (A) A quadrilateral cannot be square unless it has four equal sides, but having four equal sides doesn't guarantee a quadrilateral to be a square.
A necessary condition is one without which the result cannot happen; a sufficient condition is one that by itself guarantees the result. Every square has four equal sides (necessary), but four equal sides do not make a square, because a rhombus also has four equal sides; right angles are needed as well (so the condition is not sufficient). Option A says exactly this. Options B and C reverse the meaning by denying that squares have equal sides, and D denies any connection. In symbols, 'P is necessary for Q' means Q implies P, and 'P is sufficient for Q' means P implies Q.