Engineering
Mathematics
Conditional Probability
Question
For two events A & B, which of the following is/are correct
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Solution
Given A, B are two events.
(1) (A∪B)∩B = (A∪B) + B − ((A∪B)∪B)
⇒ (A∪B)∩B = (A∪B) + B − (A∪B) = B
⇒ (A∪B)∩B) = B
(2) (A∪B)C∩BC = ((AC∩B)∪BC) = (AC∩BC)
⇒ (A∪B)C∩BC = (AC∩BC) = (A∪B)C
(3) AC∩(A∩B) = ϕ (since AC indicates excluding Aeverything in the set, whereas A∩B indicates common between A and B. so intersection of both is a null set)
AC∩(A∩B)∩BC = ϕ ∩BC = ϕ
(4) (AC∩B)∩(A∪B) = (B − (A∩B))∩(A∪B) = (B − (A∩B)
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