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

Sum

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

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Solution

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, ∞)`

Concept: Types of Sets
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Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 5 Sets and Relations
Exercise 5.1 | Q 15. (viii) | Page 98
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