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Sets are collections of well-defined objects that can be represented symbolically. A set contains elements and its size is represented by a cardinal number in curly brackets. There are different ways to represent sets, including roster form which lists elements and set-builder form which uses properties to define elements. Some common types of sets are empty/null sets containing no elements, finite sets with a limited number of elements, and infinite sets with an unlimited number. Examples of standard sets used in mathematics include the sets of natural numbers, integers, primes, and rational numbers.
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This document discusses sets and set theory. It defines what a set is, the different types of sets, and how sets are represented. The key points are:
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The document introduces basic concepts of set theory, including:
- A set is a collection of distinct objects called elements or members.
- Special sets include the natural numbers, integers, rational numbers, and real numbers.
- Types of sets include subsets, equal sets, empty sets, singleton sets, finite sets, infinite sets, disjoint sets, power sets, and universal sets.
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math.pptx
- 1. SETS They are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1,2,3,4,5,6,7,8,…..∞}
- 3. Roster Form Listing the elements of a set inside a pair of braces { } is called the roster form. (i) Let A be the set of even natural numbers less than 11. In roster form we write A = {2, 4, 6, 8, 10} (ii) A = {x : x is an integer and- 1≤ x < 5} In roster form we write A = {-1, 0,1, 2, 3, 4}
- 4. Set Builder Form Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy. Reading Notation : ‘|’or ‘:’ such that A = { x : x is a letter in the word dictionary } We read it as “A is the set of all x such that x is a letter in the word dictionary” For example, (i) N = "x : x is a natural number, (ii) P = "x : x is a prime number less than 100, (iii) A = "x : x is a letter in the English alphabet,
- 5. What are the types of Sets? A set has many types, such as; 1.Empty Set or Null set: It has no element present in it. Example: A = {} is a null set. 2.Finite Set: It has a limited number of elements. Example: A = {1,2,3,4} 3.Infinite Set: It has an infinite number of elements. Example: A = {x: x is the set of all whole numbers} 4.Equal Set: Two sets which have the same members. Example: A = {1,2,5} and B={2,5,1}: Set A = Set B 5.Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B . Example: A={1,2}, B={1,2,3,4}, then A ⊆ B
- 6. P - denoting the set of all primes. N - denoting the set of all natural numbers. Z - denoting the set of all integers. z⁺- denoting the set of all positive integers. Q - denoting the set of all rational numbers. Q⁺- denoting the set of all positive rational numbers.
- 7. THANKYOU