 Hello and welcome to the session. In this session we will discuss types of sets. The first type of set that we are going to discuss is finite set. A finite set is a set whose elements can be counted. For example, a set A which is equal to the set containing the elements 1, 2, 3, 4, 5, 6. Now since we can count the elements of the set A, so A is a finite set. The second type of set that we will discuss is infinite set. Infinite set is a set which contains uncountable elements. For example, the set P which is equal to the set of prime numbers. Now since there exist infinite number of prime numbers, so the elements of the set P cannot be counted. Hence P is an infinite set. Next is singleton set. Singleton set is a set having only one element. For example, set A which is equal to the set containing x such that x is a natural number, 3 is less than x is less than 5. So the set A contains all the natural numbers between 3 and 5. We know that pole is the only natural number between 3 and 5. So the set A contains the element 4. That is A contains only one element. Hence A is a singleton set. Next is empty or null set. An empty or null set is a set that contains no element. It is denoted by 5 or pair of curly bases. The set containing 5 does not represent an empty set and the set containing 0 is not a null set as it contains the element 0. For example, set A which is equal to the set containing rectangles having 6 sides. We know that all rectangles have 4 sides so there are no rectangles having 6 sides. Hence A is an empty set. Consider another example. Let B is equal to the set containing x such that x is a prime number, 3 is less than x is less than 5. So the set B contains all the prime numbers between 3 and 5. We know that there exists no prime number between 3 and 5. So B contains no elements hence B is an empty set. Next is equal sets. Two sets A and B are set to be equal if they have exactly same elements. That is two sets A and B are set to be equal if an element of A is an element of B and vice versa. We write it as A equals B. For example, let A is equal to set of letters of the word Rome and B is equal to set of letters of the word then A is equal to the set containing the letters R, O, M, E and B is equal to the set containing the letters M, O, R, E. So the sets A and B contain same elements irrespective of their order. Hence we can say that A and B are equal sets. Now before we discuss equivalent sets let us see what a cardinal number of a set is. The cardinal number of a set is the number of distinct elements present in a finite set A. It is denoted by N of A. For example let P is equal to set of letters of the word sweet. Now the distinct letters of the word sweet are S, W, E, T. So P is equal to the set containing the letters S, W, E, T. We can see that the number of elements in the set P is 4. So the cardinal number of P is equal to 4. Next we have equivalent sets. Two sets A and B contain the same number of elements then A and B are equivalent sets. We indicate such sets as A is equivalent to B. For example let A is equal to the set containing the elements 1, 2, 3, 4, 5 and B is equal to the set containing the elements A, E, I, O, U. We can see that both the sets A and B contain five elements. So cardinal number of A is equal to 5 and cardinal number of B is equal to 5. So A and B are equivalent sets. We may also say that all equal sets are equivalent sets but all equivalent sets are not equal sets. Next is disjoint sets. Disjoint sets are the sets which do not have any element in common. That is any element of a set A is not in set B and any element of set B is not in set A. For example consider the set A which is equal to the set containing the elements 1, 2, 3, 4 and B is equal to the set containing the elements 5, 6, 7, 8. We can see that all the elements in the two sets A and B are different. So the two sets A and B do not have any element in common. So A and B are disjoint sets. Now the next is overlapping sets. Two sets are overlapping sets if they contain at least one element in common. For example let A is equal to the set containing the elements 9, 10, 11 and B is equal to the set containing the elements 5, 10, 15. The common element in both the sets is 10. A and B are overlapping sets. So in this session we learnt about types of sets which are finite set, infinite set, singleton set, empty or null set, equal sets, equivalent sets, disjoint sets and overlapping sets. With this we end our session. Hope you enjoyed the session.