Question

Use
Upper A equals StartSet 3 ,4 , 7 EndSetA={3,4,7}
and
Upper B equals StartSet 1 , 2 , 5 , 8 EndSetB={1,2,5,8}
to find the set
left parenthesis Upper A intersect Upper B right parenthesis union left parenthesis Upper A intersect Upper B prime right parenthesis(A ∩ B) ∪ A ∩ B′
within the universal set
Uequals=​{0,1,2,
. . .​ ,10}.
left parenthesis Upper A intersect Upper B right parenthesis union left parenthesis Upper A intersect Upper B prime right parenthesis equals(A ∩ B) ∪ A ∩ B′=
(Use ascending​ order.)

Answer 1

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}