Question

If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B' ∩ C'

Answer 1

A = (–7, 3] = {x / x ∈ R, –7 < x ≤ 3}

B = [2, 6] = {x / x ∈ R, 2 ≤ x ≤ 6}

C = [4, 9] = {x / x ∈ R, 4 ≤ x ≤ 9}

B' = R – B

= R – {x / x ∈ R, 4 ≤ x ≤ 9}

= {x / x ∈ R, x < 2 or x > 6}

C' = R – C

=  R – {x / x ∈ R, 4 ≤ x ≤ 9}

= {x / x ∈ R, x < 4 or x > 9}

∴ B' ∩ C' = {x / x ∈ R, x < 2 or x > 6} ∩ {x / x ∈ R, x < 4 or x > 9}

= {x / x ∈ R, x < 2 or x > 9}

= `(- ∞, 2) ∪ (9, ∞)`