Question

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

Answer 1

Correct Answer - Option 1 : P ∪ Q

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