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Assertion (A): 0 is the multiplicative identity for whole numbers. Reason (R): a × 1 = a for every whole number a. Which option is correct?

Class 6Whole NumbersWhole Numbers
  • ABoth A and R are true and R explains A
  • BA is false, but R is true
  • CBoth A and R are false
  • DA is true, but R is false

Step-by-Step Solution

The multiplicative identity is 1, not 0 (since a × 1 = a, but a × 0 = 0). So A is false. R correctly states a × 1 = a, so R is true. Hence A is false but R is true.
Answer: B) A is false, but R is true

Key idea: Closure: when an operation 'stays inside' the whole numbers

Adding two whole numbers always gives a whole number — addition is **closed** on whole numbers. Multiplying two whole numbers always gives a whole number — multiplication is **closed** too. But subtraction is **not** closed: 5 − 7 = −2, which is not a whole number. Division is also not closed: 7 ÷ 2 = 3.5, not a whole number. Closure is the property that lets us trust an operation never to take us 'outside' the world of whole numbers.

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