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?

Answer 1

(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