If A = { x : x is a multiple of 3} and B = (x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set?

where A \ B: Set A with the elements that are not in set B removed. This is also known as the set difference between A and B.

This question was previously asked in
NDA (Held On: 19 Apr 2015) Maths Previous Year paper
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  1. (A \ B) ∪ C
  2. (A \ B) \ C
  3. (A ∩ B)∩ C
  4. (A ∩ B) \ C

Answer (Detailed Solution Below)

Option 4 : (A ∩ B) \ C
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Detailed Solution

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Concept:

  • Null set is the set that does not contain anything.
  • In mathematical sets, the null set, also called the empty set,
  • It is symbolized or { }.


Calculation:

Given:

A = {x : x is a multiple of 3}

∴ A = {3, 6, 9, 12, 15, 18, 24…}

B = {x : x is a multiple of 4}

∴ B = {4, 8, 12, 16, 20, 24, 28, 32 ...}

C = {x : x is a multiple of 12}

∴ C = {12, 24, 36, 48, 60, 72, 84, 96 ...}

Now,

A∩B = {12, 24 ...} = C

∴ (A∩B) \ C = { } = Null set

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