Question

If A = {1, 2, 3, 4, 5}

B = {2, 4, 6, 8}

and C = {3, 4, 5, 6}

Verify : A - (B ∪ C) = (A - B) ∩ (A - C)

Answer 1

A = {1, 2, 3, 4, 5}

B = {2, 4, 6, 8}

C = {3, 4, 5, 6}

B ∪ C = {2, 4, 6, 8} ∪ {3, 4, 5, 6}

= {2, 3, 4, 5, 6, 8}

A - (B ∪ C) = {1, 2, 3, 4, 5} - {2, 3, 4, 5, 6, 8}

= {1}

A - B = {1, 2, 3, 4, 5} - {2, 4, 6, 8}

= {1, 3, 5}

A - C = {1, 2, 3, 4, 5} - {3, 4, 6, 8}

= {1,2}

∴ (A - B) ∩ (A - C) = {1, 3, 5} - {1,2}

= {1}

∴  A - (B ∪ C) = (A - B) ∩ (A - C)