# If A = {x : x <sp

Natural numbers start from 1

A = {1, 2, 3, 4, 5, 6, 7}

B = {2, 3, 5, 7}

C = {1, 3, 5, 7, 9}

(i) B C = {3, 5, 7}
AU(B C) = {1, 2, 3, 4, 5, 6, 7}

A B = {1, 2, 3, 4, 5, 6, 7}

A C = {1, 2, 3, 4, 5, 6, 7, 9}

(A B) (A C) = {1, 23, 4, 5, 6, 7} A (B C) = (A B) (A C)

Hence proved

(ii) B C = {1, 2, 3, 5, 7, 9}

A (B C) = {1, 2, 3, 5, 7}

A B = {2, 3, 5, 7}

A C = {1, 3, 5, 7}

(A B) (A C) = {1, 2, 3, 5, 7} A (B C) = (A B) (A C)

Hence proved

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