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  1. (A – B) ∪ C
  2. (A – B) – C 
  3. (A ∩ B) ∩ C
  4. (A ∩ B) – C 
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1 Answers

Option 4 : (A ∩ B) – C 

A = {x : x is a multiple of 7} = {7, 14, 21, 28, 35………..}

B = {x : x is a multiple of 5} = {5, 10, 15, 20, 25………..}

C = {x : x is a multiple of 35} = {35, 70, 105, 140……..}

Checking all the options:

(A – B) ∪ C = {7, 14, 21, 28, 42 …..} ∪ {35, 70, 105, 140……..} = {7, 14, 21, 28, 35, 42, 49…}

Hence it is not a null set.

(A – B) – C = {7, 14, 21, 28, 42 …..} – {35, 70, 105, 140……..} = {7, 14, 21, 28, 42, 49….}

Hence it is not a null set.

(A ∩ B) ∩ C = {35, 70, 105, 140……} ∩ {35, 70, 105, 140……..} = {35, 70, 105, 140……..}

Hence it is not a null set.

(A ∩ B) – C = {35, 70, 105, 140……} – {35, 70, 105, 140……..} = ∅

Hence it is a null set.

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