# Thread: Need help with sets

1. ## Need help with sets

Hi, I'm having a bit of trouble with the following problems:

Let S = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}. List all of the elements in each of the following sets.

(a) A=[x∈S l x is even and x is a multiple of 3].

b) B=[x∈S l if x is odd, then x is a multiple of 5]

I am really confused, as I'm not sure how to solve this. For a) there is no even number in set S that is also a multiple of 3. I have attempted this question many times without any luck, and would greatly appreciate any help.

Thanks

2. As for part (a), you are almost right. There is just one number, which is even and a multiple of 3, namely 0. Certainly 0 is even, and since 3 times 0 is 0 itself, 0 is a multiple of 3.

So A = {0}.

EDIT: As for the set B, CaptainBlack is correct over what I wrote, which was:

As for B, I take the description of B to mean that x is an element of B, if x is odd, and x is a multiple of 5. Only two members of S have this property, namely -5 and 5 (because 1 times 5 is 5, and -1 times 5 is -5).

So B = {-5,5}.

3. Originally Posted by spoc21
Hi, I'm having a bit of trouble with the following problems:

Let S = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5}. List all of the elements in each of the following sets.

(a) A=[x∈S l x is even and x is a multiple of 3].

b) B=[x∈S l if x is odd, then x is a multiple of 5]

I am really confused, as I'm not sure how to solve this. For a) there is no even number in set S that is also a multiple of 3. I have attempted this question many times without any luck, and would greatly appreciate any help.

Thanks
B consists of all even elements of S and those odd elements which are multiples of 5.

B=[x∈S l if x is odd, then x is a multiple of 5] reads as:

B is the set of elements x of S such that if x is odd it is a multiple of 5.

CB