Answer
(A∩B)∪(A∩C) = {1,3,5}
Work Step by Step
A={1,3,5,7}
B={1,2,3}
C={2,3,4,5,6}
TO FIND (A∩B)∪(A∩C) Let's first find (A∩B) and (A∩C)
A∩B = {1,3,5,7} ∩ {1,2,3} = {1,3}
(Common elements of A and B)
A∩C = {1,3,5,7} ∩ {2,3,4,5,6} = {3,5}
(Common elements of A and C)
(A∩B)∪(A∩C) = {1,3} ∪ {3,5} = {1,3,5}
(All elements of (A∩B) and the elements of (A∩C) which are not there in (A∩B))
(A∩B)∪(A∩C) = {1,3,5}
