Question

A{1,2,3,4}, B={2,3,4,5},C={3,4,5,6} the show that AUNION(BINTERSECTION C)= (A UNION B) INTERSECTION (A UNION C)

Answer 1

HELLO!!

ANSWER:

A U (B ^ C) = (A U B) ^ (A U C)

HENCE PROVED.

EXPLANATION:

NOTE- "U" denotes union of sets and "^" denotes intersection of sets.

GIVEN:

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

TO SHOW:

A U (B ^ C) = (A U B) ^ (A U C)

SOLUTION:

LHS:

A U (B ^ C):

B ^ C = {3,4,5}

A U (B ^ C) = {1,2,3,4,5}
______________________

RHS:

(A U B) ^ (A U C):

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

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

(A U B) ^ (A U C) = {1,2,3,4,5}
_______________________

LHS = RHS

HENCE PROVED.

HOPE IT HELPS YOU!!