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

Relevance
  • 6 years ago
    Favorite 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

  • None
    Lv 7
    6 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?

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