#### Answer

(A∪B)∩(A∪C) = {1,2,3,5,7}

#### 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} = {1,2,3,5,7}
(All elements of A and the elements of B which are not in A)
A∪C = {1,3,5,7} ∪ {2,3,4,5,6} = {1,2,3,4,5,6,7}
(All elements of A and the elements of C which are not in A)
(A∪B)∩(A∪C) = {1,2,3,5,7} ∩ {1,2,3,4,5,6,7} = {1,2,3,5,7}
(Common elements of (A∪B) and (A∪C))
Thus (A∪B)∩(A∪C) = {1,2,3,5,7}