Let U = R (the set of all real numbers) If A = {x : x∈R, 0 < x < 2}, B = {x : x∈R, 1

Engineering

Mathematics

Conditional Probability

Question

Let U = R (the set of all real numbers) If A = {x : x∈R, 0 < x < 2}, B = {x : x∈R, 1 < x ≤ 3}, then

A∪B = {x : x∈R and 0 < x ≤ 3}

A∩B = {x : x∈R and 1 < x < 2}

A − B = {x : x∈R and 0 < x ≤ 1}

all of these

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We have, A′ = R − A = {x : x∈R and x∉A}

= {x : (x∈R and x ≥ 2) or (x∈R and x ≤ 0)}

= {x : x∈R and x ≤ 2} ∪{x : x∈R and x ≤ 0}

Similarly, B′ = {x : x∈R and x ≤ 1}∪{x : x∈R and x > 3

∴ A∪B = {x : x∈R and 0 < x ≤ 3}

A∩B = {x : x∈R and x < x < 2}

A − B = {x : x∈R and 0 < x ≤ 1}

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