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Question
Use the given diagram to find:
(i) A ∪ (B ∩ C)
(ii) B - (A - C)
(iii) A - B
(iv) A ∩ B'
Is A ∩ B' = A - B?
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Solution
(i) B ∩ C = {d, e, f, g, h,j} ∩ {h, i, j, k, l}
= {h, j}
∴ A ∪ (B ∩ C) = {a, b, c, d, g, h, i} ∪ {h, j}
= {a, b, c, d, g, h, i, j}
(ii) A - C = {a, b, c, d, g, h, i} - {h, i, j, k, l}
= {a, b, c, d, g}
∴ B - (A - C) = {d, e, f, g, h, j} - {a, b, c, d, g}
= {e, f, h, j}
(iii) A - B = {a, b, c, d, g, h, i} - {d, e, f, g, h, j}
⇒ A - B = {a, b, c, i} ...(I)
(iv) B' = {a, b, c ,i, k, l, m, n, p}
A ∩ B' = {a, b, c, d, g, h, i} ∩ {a, b, c, i, k, l, m, n, p}
⇒ A ∩ B' = {a, b, c, i} ...(II)
From I and II we can conclude A ∩ B' = A - B
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