let A and B be subsets of a universal set U={a,b,c,d,1,2,3,4}, A={a,c,1,2}, A∩B= {c,1,2} and AUB={a,c,d,1,2,4}. Find B'

Question

Solve for B'

Answer 1

B' = elements of U that aren't in B

if AUB = {c,1,2} and U includes a through d and 1 through 4

then B' possibilities are a,b,d and 3,4, but AUB doesn't have a, b or 3

so that narrows it down to a,b and 3

which means

B' = {a, b, 3}

draw a Venn diagram to see this better

Answer 2

A∪B = A + B - A∩B

 

{a,c,d,1,2,4} = {a,c,1,2} + B - {c,1,2}

 

B = {c,d,1,2,4}

 

B' = elements of U that aren't in B

 

B' ={a,b,3}

 

you might get another tutor's input if this isn't clear