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

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If \(A = \{-2, 0, 1, 3, 5\}\), \(B = \{-1, 0, 2, 5, 6\}\) and \(C = \{-1, 2, 5, 6, 7\}\), show that \(A - (B \cup C) = (A - B) \cap (A - C)\).

Proof:

\(B \cup C =\)

\{i, i, i, i, i, i\}

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

\{i, i, i\}

---- (\(1\))

\(A - B =\)

\{i, i, i\}

\(A - C =\)

\{i, i, i, i\}

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

\{i, i, i\}

---- (\(2\))

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

Hence, we proved.

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12. Five mark exercise problems IV