Five mark exercise problems III — task. Mathematics State Board, Class 9.

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If \(A = \{b, c, e, g, h\}\), \(B = \{a, c, d, g, i\}\) and \(C = \{a, d, e, g, h\}\), show that \(A - (B \cap C) = (A - B) \cup (A - C)\).

Proof:

\(B \cap C =\)

\{i, i, i\}

\(A - (B \cap C) =\)

\{i, i, i, i\}

---- (\(1\))

\(A - B =\)

\{i, i, i\}

\(A - C =\)

\{i, i\}

\((A - B) \cup (A - C) =\)

\{i, i, i, i\}

---- (\(2\))

From equations (\(1\)) and (\(2\)), \(A - (B \cap C) = (A - B) \cup (A - C)\).

Hence, we proved.

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11. Five mark exercise problems III