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Properties of Set Operation

If A = b, c, ...

Question

If A = {b, c, e, g, h}, B = {a, c, d, g, i} and C = {a, d, e, g, h}, then show that A – (B ∩ C) = (A – B) ∪ (A – C).

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Solution

A = {b, c, e, g, h}
B = {a, c, d, g, i}
C = {a, d, e, g, h}

Now B ∩ C = {a, d, g} [0.5 marks]
So A – (B ∩ C) = {b, c, e, g, h} – {a, d, g}
= {b, c, e, h} … (1) [0.5 marks]
A - B = {b, c, e, g, h} – {a, c, d, g, i}
= {b, e, h} [0.5 marks]
A – C = {b, c, e, g, h} – {a, d, e, g, h}
= {b, c} [0.5 marks]

(A – B) ∪ (A – C) = {b, c, e, h} … (2) [0.5 marks]

From (1) and (2) it is verified that,
A – (B ∩ C) = (A – B) ∪ (A – C) [0.5 marks]

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