Last Updated on September 10, 2026 by Maged kamel
Introduction to Roster notation.
Discrete math symbols.
For discrete math, we can consult the NCEES FE Exam Handbook to find the discrete math subjects. Page 21 includes the symbols. A small x is part of X or a member of X in this subject. The second symbol is the empty set, denoted by phi. S is a subset of T. The following symbol for S is a proper subset of T. The next symbol is for the empty set, followed by a subset of T.
Roster notation.
We start with Roster notation. Merriam-Webster defines a roster as a list of people or things that belong to a particular group. There are symbols with different shapes.
List the elements of a set inside braces, separated by commas. As discussed for the natural numbers, according to Roster notation, the set is enclosed in curly braces on both the left and right, and the number 1 is included in the set of counting numbers: {1, 2, 3, 4, 5}.
The previous list was for the whole numbers, but we add 0. We have a continuum for both the natural and whole numbers.
We have already discussed the Expression of Integers: zero, positive, and negative values.
As for rational numbers, we use braces { at the left and right}, which include a/b, where a and b are integers. Expression deal with positive or negative values.
That is why the definition states that the numerator and denominator are integers. You can have zero in the numerator and express it as a/b, where a and b are Integers. Still, the denominator should not be = 0; it is written as b0 to avoid expressing infinity.
∈ is an element that belongs to ∉ is not an element or does not belong to it is the same previous symbol ∈ but with an inclined line.
Some samples for Roster notation.
For example, 3 belongs to the set {1, 2, 3, 4}.
3 is indeed an element of that group, but 1/3 does not belong to the previous group, {11, 2, 3, 4,5}5}.
Then it is written as ⊄. The number 50 is a part of X, such that the symbol expresses that it is an Integer.
The statement is true if x, expressed by the symbol |, which starts at 0 and extends to 50, is a positive irrational number. It is said that 50 is an element of x, provided that x is an integer.
For -5. Does -5 belong to the family of rational numbers? Yes, since a rational number can be written as -5/1. Any number can be considered rational if the denominator is 1, so -5 belongs to the set of all x values such that x is a rational number.
Solved Examples 1 and 2- for Roster notation.
Let us check example #1. Let G be the set of whole numbers <10. We have explained that whole numbers include 0 and all positive numbers. To write the Expression in set notation, we start with the left brace {, write 0, then 1, 2, 3, 4, 5, and end with 9, then the right brace }.
For example #2. Let X be the set of all odd numbers that are < 12. The odd numbers are 1,3,5,7,9,11,13. We consider these odd numbers. 0 is not an odd number; it is not included. We start with the left brace {, write 1, then 1, 3, 5, 7, 9, 11, and finish with the right brace }.
Example 3 for Roster notation.
In example #, which of the following sets of whole numbers are < 10? There are three options; the first is Expression of Capital C.
You must check the set of whole numbers, as discussed: the set of whole numbers includes 0, 1, 2, 3, 4, without fractions. This is required only for odd numbers; it is a true selection if it is required for integers < 10, but it is OK to write only odd numbers.
The first choice is not correct. We move on to the second selection: {6, 6, 86, 8}. This list includes all the even numbers less than 10. This option is not {1, 3, 5, 7, 9}.
This collection has all odd numbers less than 10 and positive Whole numbers.
The fourth choice is not a true selection. The third option is correct.
Equality of sets.
The next item is whether we have two sets and want to check whether they are equal.
The first set is A = {1, 3, 5, 7}. The second set is B = {3, 7, 1, 5}.
The two sets have the same number of elements; the same numbers appear in both. Since order doesn’t matter, A = B. The selection is correct; why?
Since all elements of A are the same as the elements in B, let us check example # 4, with God’s will. Let R be the set of all whole numbers <5.
LS = S4, 0, 2, 3, 13,1}, same number of elements, and the next question w l bwhatwhat at is the set of all whole numb e r?5?? The whole numbers start with 0 and continue with 1, 2, 3, and 4, and can be represented by R = {0, 1, 2, 3, 4}.
For = S {4,0,2,3,1}, the same number of elements and the same figures; thus, R and S are equal sets.
Examine the set, whether finite or infinite.
The following item examines whether the set is finite or infinite. Finite is limited, while infinite is not limited. At the same Time, write the set of all Integers.
We write the set as {…, -2, -1, 0, -1, 0, 1, 2, 3…} 4,; the; set of integers is infinite since it is continuous at both ends. While for item b), the set of all natural numbers between (0,5) {1,2,3,4}{,1,2,3,4} is an example of a finite set.
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For an external link to Math Is Fun, please see the Venn Diagram link.
For the next post, here are the subsets of sets and the Venn diagram.
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