Here you will learn what is the symmetric difference of two sets with venn diagram and examples. Let’s begin – Symmetric Difference of Two Sets Definition : Let A and B be two sets. The symmetric difference of sets A and B is the set (A – B) \(\cup\) (B – A) and is denoted …
Symmetric Difference of Two Sets – Venn Diagram and Examples Read More »
Here you will learn what is the difference of two sets with venn diagram and examples. Let’s begin – What is Difference of Two Sets ? Definition : Let A and B be two sets. The difference of A and B, written as A – B, is the set of all those elements of A …
Here you will learn what is the union of sets with definition and venn diagram representation and examples. Let’s begin – What is the Union of Sets ? Definition : Let A and B be two sets. The union of A and B is the set of all those elements which belong either to A …
Union of Sets – Definition and Venn Diagram with Examples Read More »
Here you will learn what is the intersection of sets with definition and venn diagram and examples. Let’s begin – What is the Intersection of Sets ? Definition : Let A and B be two sets. The intersection of A and B is the set of all those elements that belong to both A and …
Intersection of Sets – Definition and Venn Diagram with Examples Read More »
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 …
What are Disjoint Sets – Venn Diagram and Examples Read More »
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) = { …
What is Power Set – Definition, Formula and Examples Read More »
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 …
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.
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 …
What are Subsets in Math – Proper and Improper Subsets Read More »
