Question

A=(1,2,3,4,5,6),B=(4,6,7,8,9,10)and C=(4,6,10,12) then prove that

Answer 1

we are given
A={1,2,3,4,5,6}; B={4,6,7,8,9,10}
C={4,6,10,12}

(1) proof:
LHS=A u (B n C)={1,2,3,4,5,6} u [{4,6,7,8,9,10} n {4,6,10,12}]
= {1,2,3,4,5,6} u {4,6,10}
={1,2,3,4,5,6,10}------------(1)
RHS= (A u B) n (A u C)
=[{1,2,3,4,5,6} u {4,6,7,8,9,10}] n [{1,2,3,4,5,6} u {4,6,10,12}]
={1,2,3,4,5,6,7,8,9,10} n {1,2,3,4,5,6,10,12}
={1,2,3,4,5,6,10}--------------(2)
LHS=RHS

(2)
LHS=A U (B U C)
.={1,2,3,4,5,6} U [{4,6,7,8,9,10} U {4,6,10,12}]
={1,2,3,4,5,6} U {4,6,7,8,9,10,12}
={1,2,3,4,5,6,7,8,9,10,12}--------------(1)
RHS=(A U B) U (A U C)
=[{1,2,3,4,5,6} U {4,6,7,8,9,10}] U [{1,2,3,4,5,6} U {4,6,10,12}]
={1,2,3,4,5,6,7,8,9,10} U {1,2,3,4,5,6,10,12}
={1,2,3,4,5,6,7,8,9,10,12}-------------(2)

LHS=RHS