# Notation to define specific elements from multiple sets in a superset

• May 7th 2011, 01:03 PM
zeromus
Notation to define specific elements from multiple sets in a superset
I'm trying to come up with the proper and concise notation to denote all the elements shown in bold red in the following sets where T is the superset containing A,B,C,D,E. Also the elements in each set are not necessarily the same, this is just how I've written them, so the 1 in set A is not the same as the 1 in set B and so on.

T { A B C D E }
A { 1 2 3 4 5 6 7 8 9 10 11 12 }
B { 1 2 3 4 5 6 }
C { 1 2 3 4 5 6 7 8 9 10 11 12 }
D { 1 2 3 4 5 6 7 8 9 10 11 12 }
E { 1 2 3 4 5 6 7 8 9 10 11 12 }

I've come up with the following possible solutions so far but they're all probably wrong with all of them.

(x<7) ∧ ¬B

{x∈T:¬B ∧ x<7}

{x∈T:x∉B; x<7}

{x|x<7;x∉B}
• May 8th 2011, 03:49 AM
HappyJoe
First of all, I haven't seen the tiny square before, what does it mean? Just "and"? I'm also curious as to who (which book) uses this notation.

When you write $\{x\in T : \ldots\}$, then you don't get to consider the right sets. The elements in T are A, B, C, D and E, so the set $\{x\in T : \ldots\}$ is necessarily a subset of $\{A, B, C, D, E\}$, no matter what the condition for the set is.

I would write

$\{x\in S|S\in T, S\neq B, x<7\},$

where I'm trying not to worry about what it means, when you say that the number 1 in A is not the same as the number 1 in B. The important thing is that the first six elements of A are exactly the elements of A that are less than 7, and likewise for C, D, and E.
• May 8th 2011, 07:41 PM
zeromus
Thanks a lot for the solution. I'm glad I was somewhat close.

Also the tiny square, as with all the characters in my attempted solutions, was actually just some unicode plaintext that must not have displayed correctly in your browser. And yes, it was the Logical AND /\ symbol.