Let P̅ and Q̅ denote the complements of two sets P and Q. Then the set (P - Q) ∪ (Q - P) ∪ (P ∩ Q) is

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  1. P ∪ Q
  2. P̅ ∪ Q̅ 
  3. P ∩ Q
  4. P̅ ∩ Q̅ 

Answer (Detailed Solution Below)

Option 1 : P ∪ Q
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NIMCET 2020 Official Paper
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Detailed Solution

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Concept:

P - Q = The set of elements which belong to P but not to Q

P U Q = The set which consists of all elements of P and all elements of Q, the common elements being taken only once.

P ∩ Q = The set of all elements which are common to both A and B.

Calculation:

let us suppose P = {1, 2, 3, 4} and Q = {3, 4, 5, 6}

⇒ P - Q = {1, 2}

⇒ Q - P = {5, 6}

⇒ P U Q = {1, 2, 3, 4, 5, 6}

⇒ P ∩ Q = {3, 4}

⇒ (P - Q) ∪ (Q - P) ∪ (P ∩ Q) = {1, 2} U {5, 6} U {3, 4} = {1, 2, 3, 4, 5, 6} = P U Q

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