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5 cze 2024 · Sets are a well-defined collection of objects. Objects that a set contains are called the elements of the set. We can also consider sets as collections of elements that have a common feature. For example, the collection of even numbers is called the set of even numbers.
There are various types of sets like – finite and infinite sets, equal and equivalent sets, a null set, etc. Further, there are a subset and proper subset, power set, universal set, disjoint sets, etc depending on the characteristics of the sets.
What are the Properties of Sets in Set-Theory? Different properties associated with sets in math are, Commutative Property: A U B = B U A and A ∩ B = B ∩ A; Associative Property: (A ∩ B) ∩ C = A ∩ (B ∩ C) and (A U B) U C = A U (B U C) Distributive Property: A U (B ∩ C) = (A U B) ∩ (A U C) and A ∩ (B U C) = (A ∩ B) U (A ∩ C)
Different types of sets are classified according to the number of elements they have. Basically, sets are the collection of distinct elements of the same type. For example, a basket of apples, a tea set, a set of real numbers, natural numbers, etc. Let us learn the types of sets here in this article. Also, read:
Sets can be described in a number of different ways: by roster, by set-builder notation, by interval notation, by graphing on a number line, and by Venn diagrams. Sets are typically designated with capital letters.
Types of Sets. Let’s discuss different types of sets. Singleton Sets. When a set has only one element, it is known as a singleton set. Set $\text{A} = \left\{ \text{x}\; |\; \text{x}\; \text{is a whole number between}\;12\; \text{and}\;14\right\} = \left\{13\right\}$. Null or Empty Sets
