# Set Theory Problem

• Feb 13th 2007, 01:05 PM
jtc4zH
Set Theory Problem
I'm not sure if I got this right or not:

Let A = {n is in Z such that n = 5r for some integer r}
and
Let B = {m is in Z such that m = 20s for some integer s}

* Z is the set of all integers

1) Is A a subset of B?
2) Is B a subset of A?

My reasoning:
1) No (because every time r is odd there is a new value of n in A which does not appear in B)

2) Yes (because no matter what s is there is a m value in B which matches a n value in A)

Is my reasoning sound for these? Thanks for the help!
• Feb 13th 2007, 01:34 PM
Plato
They are correct and the reasons work.
• Feb 13th 2007, 03:31 PM
Soroban
Hello, jtc4zH!

Thought I'd test out some codes . . .

Let .A .= .{n ε Z | n = 5r for some r ε Z}
Let .B .= .{m ε Z | m = 20s for some s ε Z}

The code of the usual "membership" symbol doesn't work.
The number is 8712 . . . precede it with &# and follow it with ; (semicolon).

This fancy ε has code &# 949 ; .without the spaces.

1) Is A ⊄ B ?
2) Is B ⊄ A ?

Neither 8836 (subset) nor 8834 (proper subset) works here.

The same is true for 8704 (inverted A) and 8707 (backward E)
. . and 8709 (null set) . . . very disappointing.

• Feb 14th 2007, 12:37 PM
jtc4zH
Cool, I will try to use these next time if I remember!