Respuesta :
Given:
The universal set is,
[tex]U=\lbrace2,3,6,7,8\rbrace[/tex]The set C is,
[tex]C=\lbrace6,8\rbrace[/tex]The set D is,
[tex]D=\lbrace6,7\rbrace[/tex]Required:
To find the sets in roster form.
[tex]\begin{gathered} (a)C\cup D^{\prime} \\ (b)(C\cap D)^{\prime} \end{gathered}[/tex]Explanation:
The sets given are,
[tex]\begin{gathered} U=\lbrace2,3,6,7,8\rbrace \\ C=\lbrace6,8\rbrace \\ D=\lbrace6,7\rbrace \end{gathered}[/tex]Then
(a) The set D' is,
[tex]D^{\prime}=\lbrace2,3,8\rbrace[/tex]Thus, the required set is given by,
[tex]\begin{gathered} C\cup D^{\prime}=\lbrace6,8\rbrace\cup\lbrace2,3,8\rbrace \\ \Rightarrow C\cup D^{\prime}=\lbrace2,3,6,8\rbrace \end{gathered}[/tex](b) The intersection of C and D is given by,
[tex]C\cap D=\lbrace6\rbrace[/tex]Thus, the compliment of the above set is the required set given by,
[tex](C\cap D)^{\prime}=\lbrace2,3,7,8\rbrace[/tex]Final Answer:
The required sets in roster form are,
[tex]\begin{gathered} (a)C\cup D^{\prime}=\lbrace2,3,6,8\rbrace \\ (b)(C\cap D)^{\prime}=\lbrace2,3,7,8\rbrace \end{gathered}[/tex]
