Question

If K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h} then find the following:

(K ∩ L) ∪ (K ∩ M) and verify distributive laws

Answer 1

K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}

(K ∩ L) ∪ (K ∩ M)

(K ∩ L) = {b, d)

(K ∩ M) = {a, b, d}

(K ∩ L) ∪ (K ∩ M) = {b, d} ∪ {a, b, d} = {a, b, d}

Distributive laws

K ∪ (L ∩ M) = (K ∪ L) ∩ (K ∪ M)

{a, b, c, d, e, f) = {a, b, c, d, e, f, g} ∩ {a, b, c, d, e, f, h}

= {a, b, c, d, e, f}

Thus Verified.

K ∩ (L ∪ M) = (K ∩ L) ∪ (K ∩ M)

{a, b, d} = {a, b, c, d, e, f, g} ∪ {a, b, c, d, e, f, h}

= {a, b, d}

Thus Verified.