# Thread: Finding subsets based off of given sets

1. ## Finding subsets based off of given sets

I am working on a homework assignment for school. I have come up with an answer, but I would just like to clarify what I have.

Question: Which of the following are subsets of which?
A = {n € P: n is odd}
B = {n € p: n is prime}
C = {4n + 3: n € P}
D = {x € R: x^2 - 8x + 15 = 0}

What I did before anything was factor set D, and came up with the answers {3,5}. After factoring out set D, I went ahead and plug in numbers that fit the criteria for each set. After plugging in number fitting the conditions for each set, I came up with the answer that D is a subset of A. D is a subset of B. C is a subset of A. Are these answers correct?

2. ## Re: Finding subsets based off of given sets

Originally Posted by needhelp101
I am working on a homework assignment for school. I have come up with an answer, but I would just like to clarify what I have.

Question: Which of the following are subsets of which?
A = {n € P: n is odd}
B = {n € p: n is prime}
C = {4n + 3: n € P}
D = {x € R: x^2 - 8x + 15 = 0}

What I did before anything was factor set D, and came up with the answers {3,5}. After factoring out set D, I went ahead and plug in numbers that fit the criteria for each set. After plugging in number fitting the conditions for each set, I came up with the answer that D is a subset of A. D is a subset of B. C is a subset of A. Are these answers correct?
Look at this fact $4(3)+3=15\in C~\&~15\notin A$

3. ## Re: Finding subsets based off of given sets

Plato, are you assuming "P" is the set of prime numbers? It seems to me, especially seeing "$\displaystyle B= \{n \in P: n is prime\}$" that P is intended to be the set of positive integers and 15 certainly is an odd positive integer.

needhelp101, yes, D= {3, 5} and those are positive numbers which are both odd and prime so D is a subset of both A and B. Any number of the form 4n+ 3 is odd but not necessarily prime so C is a subset of A but not B as you say. A is not a subset of B because there exist off numbers that are odd but not prime (9 for example). B is not a subset of A because there is a prime number (2) that is prime but not odd.

4. ## Re: Finding subsets based off of given sets

Originally Posted by HallsofIvy
Plato, are you assuming "P" is the set of prime numbers? It seems to me, especially seeing "$B= \{n \in P: \text{n is prime}\}$" that P is intended to be the set of positive integers and 15 certainly is an odd positive integer.
That certainly is a more logical reading of the OP.

This should serve as warning to all users the necessary to define all terms that may be miss-read in a post.

5. ## Re: Finding subsets based off of given sets

Shall we flip a coin? needhelp101, how about letting us know what "P" was intended to mean?

6. ## Re: Finding subsets based off of given sets

I do apologize for the misunderstanding which I have cause you both. I should have put in the post somewhere what each set I was dealing with. On that note, "P" is actually being represented as the set of all positive integers. My apologies, I do appreciate the help and quick replies from you all. Thank you for your help