Math question help
Hello, I am having some difficulty understanding a math problem that I know is not that difficult but it still confuses me. The question is "Is it possible for both A â� � B (A relation B) and A ∈ B (A set B) to be true." The big problem I am having is that I cannot figure out how the relation symbol and the set symbol work and since I do not have my math book yet, I am finding it difficult to figure this out via google. Any help at all would be good.
September 6, 2012
5 Comments • Newest first
[quote=charismatic]Let A equal the empty set, and let B be a set containing the empty set.
Then A is a subset of B [i]and[/i] A is an element of B.
Thus, it is possible for A to be both an element and subset of some set B.[/quote]
You're right, but the way you worded may confuse some
(if they don't know that every set contains the null set)
let A = {null}
B = {null, {null} }
then both conditions hold
A â� � B holds because element null can be found in B
A ∈B holds because {null} = A is in B
important note:
{null} is NOT the same as { {null} }
Okayy I get it now. The answer is really simple apparently lol. Thanks for the help everyone. I just needed to understand what those symbols meant a bit better and it seems more clear now.
Sideways "U" with a line under it means ---> "Subset"
That "E" is the mathematized version of the Greek letter, Epsilon.
Epsilon means "element(s) of".
So saying that A is a subset of B also means that A are elements of B.
So, yes, it is possible for A to be a subset of B and have elements in the superset of B.
[quote=bloodIsShed]let A = {a1, a2, a3, ..., an}
let B = {b1, b2, b3, ..., bn}
A â� � B means that B = {a1, a2, a3, ..., an, b1, b2, ..., bn}
that is, every element in set A can be found in set B
(and set A could be equal to set B)
A ∈ B means that B = { {a1, a2, a3, ..., an}, b1, b2, ..., bn }
A is an "element" of set B
in the second case, B is a set of sets[/quote]
Ohh okay that makes sense. But then I dont see how both could be true at the same time since A being an element in B would not be the same as A being a subset of B.
let A = {a1, a2, a3, ..., an}
let B = {b1, b2, b3, ..., bn}
A â� � B means that B = {a1, a2, a3, ..., an, b1, b2, ..., bn}
that is, every element in set A can be found in set B
(and set A could be equal to set B)
A ∈ B means that B = { {a1, a2, a3, ..., an}, b1, b2, ..., bn }
A is an "element" of set B
in the second case, B is a set of sets