Question

If A,B and C be the letters of the words, FLOWER, COMFORT and COMPUTER respectively, verify that (i) A∩(BUC) = (A∩B) U (A∩C) (ii) (A’∩ B) = (B) – (A∩B)

Answer 1

A is the set of the letters in the word college.

A={c,o,l,e,g}

B is the set of the letters in the word marriage.

B={m,a,r,i,g,e}

C is the set of the letters in the word luggage.

C={l,u,g,a,e}

B∪C={m,a,r,i,g,e,l,u}

A−(B∪C)={c,o} (1)

A−B={c,o,l}

A−C={c,o}

(A−B)∩(A−C)={c,o} (2)

From equation (1) and (2), A−(B∪C)=(A−B)∩(A−C).