Unitary Set Example

A unitary set is one that is formed by single element. It does not matter how many times this element is repeated, if there is no other type the set will be unitary. It is different from the sets as is, in which there can be an infinity of elements in varied quantities and with different characteristics. The properties that distinguish it are the following:

Unit set properties

• Cardinality: is a property that tells us the variety of elements what's up. It has a numeric value, so a set with 3 types of elements has a cardinality of 3. In the unit sets there is 1 type of element, so its cardinality is 1. All its members are the same.
• A unit set has two subsets: the empty set and himself.
• In a Venn Diagram, the intersection between two unit sets is he empty set or unitary set. It is explained below and in the following two points: an intersection is the space that carries the common elements of the two sets that are spliced.
• If the two sets are unitary, all the elements will be equal so when they are spliced ​​they will remain the same, resulting in a unitary set.
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• On the other hand, if the two sets are different, they will not have common elements to put in the intersection, so the intersection will remain as an empty set.
• If B is a unit set, all its subsets will be equal to this. At the same time, if we take into account a subset A, B will become a subset of A.
• A set such as {1, 2, 3, 4, 5} can be treated as a single element when put into another larger set. For example, if we express something like {{1, 2, 3, 4, 5}, {1, 2, 3, 4, 5}} we will have a unitary set formed by elements of this {1, 2, 3, 4, 5}.
• Also, when the elements are numbers, no matter how they express themselves, as long as they represent the same value. For example, to express the number 7, you can write: “6 + 1”, “5 + 2”, “4 + 3”, “8–1”. They are all number 7. By putting these in a set, a unitary set will be achieved. Thus, the set {"6 + 1", "5 + 2", "4 + 3", "8–1", 7} is a unitary set.

20 unit assembly examples

1. The set of natural satellites of planet Earth is a unitary set formed by the Moon.
2. The set of mammals that hatch from an egg is a unitary set formed by the platypus.
3. The set of electrons that a hydrogen atom has is a unitary set formed by one electron.
4. The set formed by the set of natural numbers from 1 to 10 is a unitary set formed by the set of natural numbers from 1 to 10.
5. The set {"3 + 3", 6, "5 + 1", "2 + 4", "9–3"} is a unitary set whose only element is the number 6.
6. The set {"8 + 3", "6 + 5", 11, "7 + 4", "14–3"} is a unitary set whose only element is the number 11.
7. The set {"5 + 3", "6 + 2", "7 + 1", 8, "9–1"} is a unitary set whose only element is the number 8.
8. The set {“2 + 3”, 5, “6–1”, “1 + 4”, “9–4”} is a unitary set whose only element is the number 5.
9. The set {"7 + 3", "6 + 4", "5 + 5", 10, "19–9"} is a unitary set whose only element is the number 10.
10. The set {"20 + 3", "16 + 7", "15 + 8", 23, "26–3"} is a unitary set whose only element is the number 23.
11. If A = {1, 3, 5, 7, 9} and B = {3, 10, 15} then the intersection of A and B (common elements) is a unit set {3}.
12. If A = {2, 4, 6, 8, 10} and B = {5, 10, 20} then the intersection of A and B (common elements) is a unit set {10}.
13. If A = {1, 2, 3, 4, 5} and B = {5, 15, 25} then the intersection of A and B (common elements) is a unit set {5}.
14. If A = {9, 18, 27, 36, 45} and B = {2, 9, 11} then the intersection of A and B (common elements) is a unit set {9}.
15. If A = {10, 20, 30, 40} and B = {5, 10, 15} then the intersection of A and B (common elements) is a unit set {10}.
16. If A = {4, 8, 12, 16, 20} and B = {20, 25, 30} then the intersection of A and B (common elements) is a unit set {20}.
17. If A = {a, b, c, d} and B = {d, e, f} then the intersection of A and B (common elements) is a unit set {d}.
18. If A = {1, 5, 6, 8} and B = {{1, 5, 6, 8}}, then B is a unit set whose only element is A.
19. If A = {11, 22, 33, 44} and B = {{11, 22, 33, 44}}, then B is a unitary set whose only element is A.
20. If A = {12, 25, 36, 48} and B = {{12, 25, 36, 48}}, then B is a unit set whose only element is A.

Follow with:

• Sets
• Union of sets