Question
Download Solution PDFLet P̅ and Q̅ denote the complements of two sets P and Q. Then the set (P - Q) ∪ (Q - P) ∪ (P ∩ Q) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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
Last updated on Jun 12, 2025
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