Question

Hey, I don’t understand this. May you please help me

Answer 1

We have

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

A={0,2,4,6,8}

B={1,3,5,7}

C={3,4,5,6}

Then let's calculate the complements

A'={1,3,5,7}

B'={0,2,4,6,8}

C'={0,1,2,7,8}

∪ means union that means that we need to put together both sets in the new set

∩ means intersection that means the new set will be composed only by the elements that share both sets that are intersecting

a.

$A\cap C=\mleft\lbrace4,6\mright\rbrace$

b.

$C^{\prime}\cup B=\mleft\lbrace0,1,2,3,5,7,8\mright\rbrace$

c.

$C^{\prime}\cap A=\mleft\lbrace0,2,8\mright\rbrace$

d.

$(A\cap C)\cup B=\mleft\lbrace1,3,4,5,6,7\mright\rbrace$

e.

$A^{\prime}\cup B^{\prime}=\mleft\lbrace U\mright\rbrace=\mleft\lbrace0,1,2,3,4,5,6,7,8\mright\rbrace$

f.

$A^{\prime}\cup(C^{\prime}\cap B)=\mleft\lbrace1,3,5,7\mright\rbrace$

g.

$(A\cap B^{\prime})\cup C^{\prime}=\mleft\lbrace0,1,2,4,6,7,8\mright\rbrace$