The total number of subsets of {A, B, C} is _____.?

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3 Answers

  • There are two choices for what to do with each element:

    – You can include it in the subset

    – You can exclude it from the subset

    2 choices for A

    2 choices for B

    2 choices for C

    Number of subsets

    = 2 x 2 x 2

    = 2^3

    = 8 subsets

    Note: That includes the set with *no* elements, the null set. It also includes the complete set of terms. For other questions, they may ask for the number of subsets with at least one element and you’d subtract 1 for the empty set. Alternatively, you might see a question asking for the number of “proper” subsets. That would exclude the complete set from being a subset. But in your case, I see no restrictions.

    Answer:

    8 subsets

    {}

    {A}

    {B}

    {C}

    {A,B}

    {A,C}

    {B,C}

    {A,B,C}

    P.S. In general, for a set with n elements, there are 2^n subsets.

  • 2^3=8

  • eight:

    {A}, {B}, {C},

    {A, B}, {B, C}, {A, C},

    {A, B, C}, {}

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