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Let U={1,2,3,4,5,6,7,8,9}, A= {1,2,3,4} and B={2,4,6,8}, then find A’ & B’.​

By Serenity

Let U={1,2,3,4,5,6,7,8,9}, A= {1,2,3,4} and B={2,4,6,8}, then find A’ & B’.​

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Serenity

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2 thoughts on “Let U={1,2,3,4,5,6,7,8,9}, A= {1,2,3,4} and B={2,4,6,8}, then find A’ & B’.​”

  2. Question:–

    Let U={1,2,3,4,5,6,7,8,9}, A= {1,2,3,4} and B={2,4,6,8}, then find A’ & B’.

    Required Answer:–

    Given:–

    [tex]\\ \sf{ \rightarrow{ U= \{1,2,3,4,5,6,7,8,9 \}}}[/tex]

    [tex] \sf{ \rightarrow{A= {1,2,3,4} }}[/tex]

    [tex] \sf{ \rightarrow{B={2,4,6,8}}} \\ \\ [/tex]

    To Find:–

    [tex] \\ \sf{ \rightarrow{ find \: A’ \: \& \: B’}} \\ \\ [/tex]

    ♡Solution:–

    First, let’s know what does A’ and B’ means in this question.

    A’ is called complement of A set. Which means A’ is a set of all elements in the given universal set U that are not in A

    Similarly, B’ is a set of all elements in the given universal set U that are not in B

    [tex] \\ \sf{Now \: let’s \: solve \: this! } \\ \\ [/tex]

    [tex] \\ \sf{ \bold{A’ }= U – A}[/tex]

    [tex] \\ \sf{ \implies{ \bold{A’ }= \{1,2,3,4,5,6,7,8,9 \} – \{1,2,3,4 \}}}[/tex]

    [tex] \\ \sf{ \implies{ \bold{A’ }= \bold{ \{5,6,7,8,9 \}}}} \\ \\ [/tex]

    [tex] \\ \rm{ \therefore{ \bold{A’ }= \red{ \{5,6,7,8,9 \}}}} \\ \\ [/tex]

    Now,

    [tex] \\ \\ \sf{ \bold{B’ }= U – B}[/tex]

    [tex] \\ \sf{ \implies{ \bold{B’} = \{1,2,3,4,5,6,7,8,9 \} – \{2,4,6,8 \}}}[/tex]

    [tex] \\ \sf{ \implies{ \bold{B’} = \bold{ \{1,3,5,7,9\}}}} \\ \\ [/tex]

    [tex] \\ \sf{ \therefore{ \bold{B’} = \red{ \{1, 3,5,7,9\}}}}\\\\[/tex]

    Therefore, A’ = {5, 6,7,8} and B’ = {1, 3,5,7,9}

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