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Thread: Need two questions involving "sets" explained to me

  1. #1
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    Need two questions involving "sets" explained to me

    My discrete math professor recently went over sets in class, but I still have a very minimal understanding of the topic. Can somebody guide me through the two problems below? My understanding of sets is so little that I don't even fully understand what the problems are asking me to do...


    Problem #1:


    Problem #2:
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  2. #2
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    Re: Need two questions involving "sets" explained to me

    Well, what about $\displaystyle U_1$? By definition $\displaystyle U_1 = \{-1, 1 \}$. What elements are in the set?

    As to $\displaystyle U_5$ check your definition about what values n can take.

    -Dan
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    Re: Need two questions involving "sets" explained to me

    Quote Originally Posted by topsquark View Post
    Well, what about $\displaystyle U_1$? By definition $\displaystyle U_1 = \{-1, 1 \}$. What elements are in the set?

    As to $\displaystyle U_5$ check your definition about what values n can take.

    -Dan
    If I understand correctly then the answers for the first problem should be:

    a) {0, 0}
    b) {-1, 1} (as you said)
    c) {5, -5}

    Is this correct? Is it actually this simple?...

    Edit: Also, just as you did with the first question, would it be possible for you to give me a starting out tip for the second problem as well?
    Last edited by ProtoflareX; Nov 29th 2015 at 01:48 PM.
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    Re: Need two questions involving "sets" explained to me

    Quote Originally Posted by ProtoflareX View Post
    If I understand correctly then the answers for the first problem should be:

    a) {0, 0}
    b) {-1, 1} (as you said)
    c) {5, -5}

    Is this correct? Is it actually this simple?...

    Edit: Also, just as you did with the first question, would it be possible for you to give me a starting out tip for the second problem as well?
    What is n equal to in c)? Check what values we can use for n...

    For 3 start off with some examples. For instance, $\displaystyle A_1 = \{ 1 \}$, $\displaystyle A_2 = \{ 1,~2 \}$, $\displaystyle A_3 = \{ 1,~2,~3 \}$. So what is $\displaystyle \cup_{i = 1}^3 A_i = A_1 \cup A_2 \cup A_3$? Can you spot the pattern?

    -Dan
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    Re: Need two questions involving "sets" explained to me

    Quote Originally Posted by ProtoflareX View Post
    If I understand correctly then the answers for the first problem should be:

    a) {0, 0}
    b) {-1, 1} (as you said)
    c) {5, -5}

    Is this correct? Is it actually this simple?...

    A starting out tip for the second problem as well?
    Your notation leaves much to be desired!
    It would be better to use $n\in\mathbb{Z}^+\cup\{0\},~U_n=\{\pm n\}$
    So $U_0=\{0\}~\&~U_1=\{\pm 1\}$

    $\bigcup\nolimits_1^n {{U_k}}=\{\pm 1,\pm 2,\cdots,\pm n\}$
    Last edited by Plato; Nov 29th 2015 at 02:18 PM.
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    Re: Need two questions involving "sets" explained to me

    Quote Originally Posted by topsquark View Post
    What is n equal to in c)? Check what values we can use for n...

    -Dan
    Unfortunately, I'm still not understanding how to do c. In c, n = -5, right? Using that information, how do I figure out what values go in the set?
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    Re: Need two questions involving "sets" explained to me

    Quote Originally Posted by ProtoflareX View Post
    Unfortunately, I'm still not understanding how to do c. In c, n = -5, right? Using that information, how do I figure out what values go in the set?
    $-5 \not \in \mathbb{Z}^+$

    thus $U_{-5}$ is undefined.
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