# Calculation of Sets

calculation of Average, Difference and Complement of Sets

## Sets

A set is a set of different objects with a common property. So about the amount of fruit in a basket or the amount of integers that are included in a list.

If the numbers $$0, 1, 4, 9$$ are contained in a set $$A$$, write $$A = {0,1,4,9}$$.

If a number is contained in a set, for example the $$4$$ in $$A$$, write $$4 ∈ A$$.

If a number is not contained in a set, for example the $$5$$ in $$A$$, write $$5 ∉ A$$.

A set is defined by the different numbers contained in the set. does not depend on the order and repetitions of the elements.

The two sets $$\{0,1,4,9\}$$ and $$\{0,0,4,0,4,4,9,0,1,4,0,9\}$$ are equal.

Two sets are equal if they contain the same elements.

A set can be empty. Remember the fruit basket mentioned above.
An empty set is represented by the symbol $$Ø$$.

A set that is contained in another set is called a subset.

$$\{1, 4\}$$ is a subset of $$\{0, 1, 4, 9\}$$

## Average and union of sets

If you compare two subsets of a larger set, you can receive both a set that consists of elements of both sets and, on the other hand, a set that consists of elements that are contained in both sets.

A set consisting of elements of two subsets is called a union of two sets.

A set consisting only of elements contained in both sets is called the average of two sets.
Example of an union
Union of the sets $$A = \{0, 1, 4, 9\}$$ und $$B = \{2, 5, 9\}$$

Write $$A ∪ B = \{1, 2, 4, 5, 9\}$$

In RedCrab Calculator use the function $$Union (A, B) = 1, 2, 4, 5, 9$$
Example of an average
Average of the sets $$A = \{0, 1, 4, 9\}$$ und $$B = \{2, 5, 9\}$$

Write $$A ∩ B = \{9\}$$

In RedCrab Calculator use the function $$Intersect (A, B) = 9$$

## Difference of a set

Set difference is a subset obtained by comparing and subtracting two subsets. The result consists only of elements of the first sets that are not contained in the second set

Difference of the sets $$A = \{0, 1, 4, 9\}$$ and $$B = \{2, 5, 9\}$$

Write $$A$$ \ $$B = \{0, 1, 4\}$$

In RedCrab Calculator use the function SetDiff $$(A, B) = 0, 1, 4$$.

## Complement

A complement is a subset obtained by comparing a subset $$A$$ with the total set $$M$$. The result consists of only elements of M that are not contained in the subset $$A$$.

Complement of the total set $$M = \{0,1,2,3,4,5,6,7,8,9,10\}$$ and the subset $$A = \{0, 1, 4, 9\}$$

Write $$M / A = \{2, 3 ,5 ,6 ,7 , 8, 10\}$$

In RedCrab Calculator use the function $$SetDiff (M, A) = 2, 3 ,5 ,6 ,7 , 8, 10$$