introduction to set theory mathematics

A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is ..

If A and B are two sets, we define their symmetric difference as the set of all elements that belong to A or to B, but not both A and B, and we denote it by A D B. Thu..

The Algebraic Properties of set operations are: Idempotent laws, Identity laws, Commutative laws, Associative laws, Distributive laws, De Morgan's Law..

Introduction - This chapter takes us much further and adds to our already existing knowledge about Ratio and Proportion. We will have to use many of the algebraic manipulations learnt earlier, use them with expertise to solve problems in this chapt..

Introduction - Lets say there are 6 frogs and 2 crabs in a pond. We can compare the number of frogs to the number of crabs in two different ways: How many more frogs than crabs are there? or How many fewer crabs than frogs are there? The answer to both the questions is same i.e. 6-2=4. Th..

Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 + 4 = ..

The total number of all possible subsets of a given set containing n elements is 2 ..

In roster method of representing a set, all the elements are listed in the set. Two sets are said to be Equivalent sets if the elements of one set can be put in one-one correspondence with the elements of the other set. T..

Set - A well-defined collection of distinct objects is called a set..

Question 1 - Question: List the elements of the following sets. Answer: i) Omit o and u from the vowels a, e, i, o, u to get {a,e,i} ii) There are exactly two such names {Karnataka, Keral..