given sets are:-

U = {0,1,2,3,4,5,6,7,8,9,10}

A = {2,3,5,7,10}

B= {3,4,0,1,9,8}

C= {2,3,1,0,6,8}

 

A.)

for B' ( it is the set which contains the elements which are present in U but not B i.e. U - B )

B'= {2,5,6,7,10}

 

B.) A U B

it contains all the elements that are present in both A and B.

A U B = {0,1,2,3,4,5,7,8,9,10}

 

c.) ( B U C )' ? A

first we will calculate B U C

B U C = {3,4,0,1,9,8} U {2,3,1,0,6,8}

= {0,1,2,3,4,6,8,9}

(B U C)' = U - (B U C)

={5,7,10}

(B U C)' ? A = {5,7,10} ? {2,3,5,7,10}

={ 5,7,10}

 

d.) ( A ? C') U B

first calculate C' = U - C = {0,1,2,3,4,5,6,7,8,9,10} - {2,3,1,0,6,8}

C' = { 4,5,7,9,10}

A ? C' = {2,3,5,7,10} ? { 4,5,7,9,10}

= {5,7,10}

(A ? C') U B = {5,7,10} U {3,4,0,1,9,8}

= { 0,1,3,4,5,7,8,9,10 }

 

e.) (B' U A') - ( A U C')

C' = { 4,5,7,9,10}

A = {2,3,5,7,10}

A U C' = {2,3,4,5,7,9,10}

B' = {2,5,6,7,10}

A' = U - A = {0,1,2,3,4,5,6,7,8,9,10} - {2,3,5,7,10}

= {0,1,4,6,8,9}

B' U A' = {2,5,6,7,10} U {0,1,4,6,8,9}

= {0,1,2,4,5,6,7,8,9,10}

(B' U A') - ( A U C') = {0,1,2,4,5,6,7,8,9,10} - {2,3,4,5,7,9,10}

={0,1,6,8}