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

1. ## 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:

2. ## 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

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

Originally Posted by topsquark
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?

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

Originally Posted by ProtoflareX
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

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

Originally Posted by ProtoflareX
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 $U_0=\{0\}~\&~U_1=\{\pm 1\}$

$\bigcup\nolimits_1^n {{U_k}}=\{\pm 1,\pm 2,\cdots,\pm n\}$

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

Originally Posted by topsquark
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?

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

Originally Posted by ProtoflareX
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.