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Which of these statements is NOT true for all whole numbers a, b and c?

Class 6Whole NumbersWhole Numbers
  • A
  • B
  • C
  • D

Step-by-Step Solution

Addition and multiplication are associative and addition is commutative, so the first three always hold. Subtraction is not associative: taking a = 10, b = 5, c = 2 gives 10 - (5 - 2) = 7 on the left but (10 - 5) - 2 = 3 on the right. Assuming the brackets can be moved in a subtraction the way they can in an addition is the trap here.
Answer: D)

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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