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 and 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. It 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}

Advertisement

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} and 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} and B = {2, 5, 9}

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