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What are the different types of sets in maths?
What is a set in math?
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Types of Sets in Maths. The different types of sets are as follows: Empty Set. The set is empty! This means that there are no elements in the set. This set is represented by ϕ or {}. An empty set is hence defined as: Definition: If a set doesn’t have any elements, it is known as an empty set or null set or void set. For e.g. consider the set,
- Singleton Sets Or Unit Sets
- Finite Sets
- Infinite Sets
- Empty Or Null Sets
- Equal Sets
- Unequal Sets
- Equivalent Sets
- Overlapping Sets
- Disjoint Sets
- Subset and Superset
A set that has only one element is called a singleton set. It is also known as a unit set because it has only one element. Example, Set A = { k | k is an integerbetween 5 and 7} which is A = {6}.
As the name implies, a set with a finite or exact countable number of elements is called a finite set. If the set is non-empty, it is called a non-empty finite set. Some examples of finite sets are: For example, Set B = {k | k is a even number less than 20}, which is B = {2,4,6,8,10,12,14,16,18}. Let us consider one more illustration, Set A = {x : ...
A set with an infinite number of elements is called an infinite set. In other words, if a given set is not finite, then it will be an infinite set. For example, A = {x : x is a real number}; there are infinite real numbers. Hence, here A is an infinite set. Let us consider one more example, Set B = {z: z is the coordinate of a point on a straight l...
A set that does not contain any element is called an empty set or a null set. An empty set is denoted using the symbol '∅'. It is read as 'phi'. Example: Set X = {}.
If two sets have the same elements in them, then they are called equal sets. Example: A = {1,3,2} and B = {1,2,3}. Here, set A and set B are equal sets. This can be represented as A = B.
If two sets have at least one element that is different, then they are unequal sets.Example: X = {4, 5, 6} and Y = {2,3,4}. Here, set X and set Y are unequal sets. This can be represented as X ≠ Y.
Two sets are said to be equivalent sets when they have the same number of elements, though the elements are different. Example: A = {7, 8, 9, 10} and B = {a,b,c,d}. Here, set A and set B are equivalent sets since n(A) = n(B)
Two sets are said to be overlapping if at least one element from set A is present in set B. Example: A = {4,5,6} B = {4,9,10}. Here, element 4 is present in set A as well as in set B. Therefore, A and B are overlapping sets.
Two sets are disjoint sets if there are no common elements in both sets. Example: A = {1,2,3,4} B = {7,8,9,10}. Here, set A and set B are disjoint sets.
For two sets A and B, if every element in set A is present in set B, then set A is a subset of set B(A ⊆ B) and B is the superset of set A(B ⊇ A). Example: A = {1,2,3} B = {1,2,3,4,5,6} A ⊆ B, since all the elements in set A are present in set B. B ⊇ A denotes that set B is the superset of set A.
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. When a set does not contain any element, it is known as a null or an ...
- What are sets formula if sets are disjoint?For disjoint sets A and B; $n(A U B) = n(A) + n(B)$ $A \\cap B = \\varnothing$ $n(A − B) = n(A)$
- Is {0} a null set ?No. There is one element inside the brackets. So, it is a singleton set, not a null set.
- What is a Cartesian Product in sets?Cartesian Product of Set A and B is defined as an ordered pair $(x, y)$ where $x \\in A$ and $y \\in B$.
- How is set theory applicable in daily lives?In real life, sets are used in bookshelves while arranging the books according to alphabetic order or genre; closets where dresses, tops, jeans are...
- Does the union of two sets include the intersection of the sets?Yes, the union of two sets includes the intersection of the sets. Union of set A and B includes the elements either in set A or in set B or in both...
In sets it does not matter what order the elements are in. Example: {1,2,3,4} is the same set as {3,1,4,2} When we say order in sets we mean the size of the set. Another (better) name for this is cardinality. A finite set has finite order (or cardinality). An infinite set has infinite order (or cardinality).
Interval Notation. Empty Set. Equality of Sets. Cardinality of Finite Sets. Summary and Review. Exercises. Introduction & Real Number Subsets. Note: Some information from section 1.5 is repeated here for a refresher; however, there is new material in this section as well and the exercises are different. (See the Table of Contents.)
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
