Answer:
(A ∩ B) ∪ A ∩ B′ = {3,4,7}
Step-by-step explanation:
Question reads:
A={3,4,7}
and
B={1,2,5,8}
to find the set
(A ∩ B) ∪ A ∩ B′
within the universal set
U ={0,1,2,. . . ,10}.
(A ∩ B) ∪ A ∩ B′=
(Use ascending order.)
Solution:
(A ∩ B) ={3,4,7}∩{1,2,5,7}={}
A∩B is the set of elements common to both...null set in this case
B' = {0,3,4,6,7,9,10} complement of B = elements of U - elem. of B
Since the operator ∩ (intersection has priority over ∪ (union), we evaluate
A ∩ B′ = {3,4,7} ∩ {0,3,4,6,7,9,10} = {3,4,7}
Therefore
(A ∩ B) ∪ A ∩ B′= {} ∪ {3,4,7} = {3,4,7}