Recall that:
[tex]\begin{gathered} A\cap C=\lbrace x|x\in A\text{ and }x\in C\rbrace, \\ A\cup C=\lbrace x|x\in A\text{ or }x\in C\rbrace. \\ C^{\prime}=U\setminus C. \end{gathered}[/tex]
Therefore:
a)
[tex]A\cap C=\lbrace4,6\rbrace.[/tex]
b) Notice that:
[tex]C^{\prime}=\lbrace0,1,2,7,8\rbrace.[/tex]
Then:
[tex]C^{\prime}\cup B=\lbrace0,1,2,3,5,7,8\rbrace.[/tex]
Answer:
(a)
[tex]A\cap C=\lbrace4,6\rbrace.[/tex]
(b)
[tex]C^{\prime}\cup B=\lbrace0,1,2,3,5,7,8\rbrace.[/tex]
