Which of the following statements is not true for the set of whole numbers?

This question was previously asked in
CTET Paper 1 - 1st Jan 2022 (English-Hindi)
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  1. a + b = b + a
  2. a – b = b – a
  3. a × b = b × a
  4. (a + b ) + c = a + (b + c)

Answer (Detailed Solution Below)

Option 2 : a – b = b – a
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Detailed Solution

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Calculation:      

Let assume that 

a = 1

b = 2

c = 3

Option 1: 

a + b = b + a

⇒ 1 + 2 = 3

⇒ 2 + 1 = 3

⇒ 3 = 3

Option 2:

a – b = b – a

⇒ 1 - 2 = -1

⇒ 2 - 1 = 1

⇒ -1 ≠ 1

Option 3:

a × b = b × a

⇒ 1 × 2 = 2

⇒ 2 × 1 = 2

⇒ 2 = 2

Option 4: 

(a + b ) + c = a + (b + c)

⇒ (1 + 2) + 3 = 6

⇒ 1 + (2 + 3) = 6

⇒ 6 = 6

The  correct option is 2 i.e. a – b = b – a
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