Set notation and symbols

Here are the most important spellings of quantities and what they meant. Everything illustrated with set diagrams.


Quantity with the elements a, b and c, so the letter then stands for everything in the parenthesis.

Illustration for a set


When every element of a set is present in another set, this is called a Subset. All elements of the set, which is on the side, on which the symbol is closed, are then also contained in the set, which is on the other side of the symbol.

Illustration for a subset in a set diagram


A complement is a set without another set, so all the elements of the right set are taken out from the left one.

Illustration for a complement in the set diagram


Cut/average size (the set containing all elements of M and N, i.e. only the elements which are present in M and N at the same time are included).

Illustration for an average or also cut in the quantity diagram


Union of sets (the set containing all elements of M or N contains all elements that are either in A or B, or both.)

Illustration for a union in the set diagram

"A across" or also "A not

These are all elements which are not in A, so all except these.

Illustration for A across or not in the set diagram


Quantities can also be specified in definitions. This determines which properties the elements of the set should have. You can see the structure of a definition here on the right/below.

  • First, x or another letter is always written, which stands for an element in the set A.
  • Behind it follows a vertical line
  • Then comes the property that this element must have to be in A
  • A=< x | x<0>-> This means that all elements in A must be less than 0
  • A=< x | x is divisor of 14>-> This means that all elements in A must be divisors of the number 14, i.e. z.B. 7.

Set Tasks

We also have par tasks in worksheets for you:

Other notations

Difference (M-N of M and N is the set of all elements contained in M but not in N)

Probability, in stochastics the P stands for probability of what is in the parenthesis.

Probability of A

Probability of A under the condition that before it B has arrived. This is the so-called conditional probability, this sets as a condition of a probability that before it another event has occurred.

"Andprobability", this is the probability that both events occur, i.e. A and B.

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