Question

Use

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}