Here you will learn what are disjoint sets in set theory with venn diagram and examples. Let’s begin – What are Disjoint Sets ? Definition : Two set A and B are said to be disjoint, if \(A \cap B\) = \(\phi\). If \(A \cap B\) \(\ne\) \(\phi\), then A and B are said to […]
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Here you will learn what is power set and its definition with examples. Let’s begin – What is Power Set ? Definition : Let A be a set. Then the collection or family of all subsets of A is called the power set of A and is denoted by P(A). That is, P(A) = {
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Here you will learn what is universal set with examples. Let’s begin – What is Universal Set ? Definition : In set theory, there always happens to be a set that contains all sets under consideration i.e. it is a superset of each of the given sets. Such a set is called universal set and
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Solution : Let A be a finite set containing n elements. Let 0 \(\le\) r \(\le\) n. Consider those subsets of A that have r elements each. We know that the number of ways in which r elements can be chosen out of n elements is \(^nC_r\). Therefore, the number of subsets of A having
Prove that the total number of subsets of a finite set containing n elements is \(2^n\). Read More »
Solution : Let A be any set and \(\phi\) be the empty set. In order to show that \(\phi\) \(\subseteq\) A, we must show that every element of \(\phi\) is an element of A also. But, \(\phi\) contains no element. So, every element of \(\phi\) is in A. Hence, \(\phi\) is the subset of A.
Prove that Empty Set is a Subset of Every Set. Read More »
Here you will learn what are subsets in math i.e. proper subsets and improper subsets with examples. Let’s begin – What are Subsets in Math ? Definition : Let A and B be two sets. If every element of A is an element of B, then A is called a subset of B. If A
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Here you will learn definition of equal sets and equivalent sets with examples. Let’s begin – Equal Sets and Equivalent Sets (i) Equal Sets : Two finite sets A and B are equivalent if their cardinal numbers are same i.e. n(A) = n(B). Where cardinal number means numbers of elements in a set. (ii) Equivalent
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Here you will learn what are finite and infinite sets, cardinality of a finite set and examples based on it. Let’s begin – Finite and Infinite Sets (i) Finite Sets A set is called a finite set if it is either void set or its element can be listed (counted, labelled) by natural numbers 1,
Finite Sets and Infinite Sets – Definition and Examples Read More »
Solution : A set consisting of a single element is called a singleton set. Example : The set {5} is a singleton set. Example : The set {x : x \(\in\) N and \(x^2\) = 9} is a singleton set equal to {3}. Note : The cardinal number of a singleton set is 1.
What is Singleton Set ? Read More »
Solution : The cardinality of a set is the number of elements in a set. For example : Let A be a set : A = {1, 2, 4, 6} Set A contains 4 elements. Therefore, Cardinality of set is 4.
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