# Need help understanding precalc symbols?

Studying for precalc. Came across this weird symbol I have never seen before.

Ā

If A = {3, 6, 9, 12}

would this mean A ≠ {3, 6, 9, 12} and that would be the acceptable answer? This is just the way I am looking at it but it seems to be wrong.

Another symbol I am looking at is this one:

http://i.imgur.com/iidxQBR.png

Again I have never seen this symbol but I know it will be on a quiz soon.

### 2 Answers

- answerINGLv 66 years agoFavorite Answer
The overscore A: Ā (I think) has traditionally been used

to refer to the complement of (in your case) a set. A U Ā should

produce the universe of elements. So depending on what your

universe is, Ā is the set of elements left, after

removing the elements of A from the universe.

∈ ∉

The epsilon (without the slash) indicates INclusion: 3 ∈ A;

The epsilon with the slash indicates EXclusion: 1 ∉ A

- NoneLv 76 years ago
In set theory, the curly brackets symbol { } encloses the members of a set, i.e., a collection of elements.

The "curved E" symbol is used to mean "is a member of the set" exactly as shown in your link.

"a∈A" means a is an element of A. If A = {3,9,14}, then 3 ∈ A and vice versa.

The curvy E with a slash through it means "is not a member of the set"

x∉A means x is not an element of A. Example: A = {3,9,14}, 1 ∉ A

The A-bar symbol Ā could mean "not A" but is not listed as a set symbol in:

http://www.rapidtables.com/math/symbols/Set_Symbol...

However, http://mathworld.wolfram.com/Bar.html tells us that the bar notation in set theory indicates either the complement Ā of a set A, or a set stripped of any structure besides order, hence the order type of the set.

In general, "complement" refers to that subset F' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of the original set. So you are more or less correct when you say that Ā ≠ {3, 6, 9, 12} ≠ {3, 6, 9, 12}, but you must recognize that this implies that Ā comprises all the other members of a set of which 3, 6, 9, 12 are elements.

More than you wanted to know, right?