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Assertion (A): The rational number is positive. Reason (R): A rational number is positive when its numerator and denominator have opposite signs. Which is correct?

Class 8Rational NumbersRational Numbers
  • ABoth A and R are true and R is the correct explanation of A
  • BA is true but R is false
  • CA is false but R is true
  • DBoth A and R are false

Step-by-Step Solution

, which is positive, so A is true. But R states the rule backwards: a rational is positive when numerator and denominator share the SAME sign, and negative when their signs are opposite. A true assertion with a false reason is the whole point of this trap.
Answer: B) A is true but R is false

Key idea: Closure of rationals

Rationals are **closed under addition, subtraction, and multiplication** — the result is always rational.

But **division is closed only if you exclude division by 0**: for any rationals a and b ≠ 0, a ÷ b is rational.

This is more than integers (which weren't closed under division at all) and more than fractions (which sometimes had subtraction lead outside the fractions). Rationals form the smallest 'nice' number system that supports all four basic operations (with the 0-divisor exception).

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