 Hello and welcome to the session. In this session, we will learn about union of sets and its properties. First of all, we should learn what is the union of sets. The union of two sets A and B is the set that contains those elements which are either in A or in B or both in A. That is A meaning B is a set containing elements X such that X belongs to B. Now let us see an example for this. Here, let A is a set containing the elements 1, 2 and 3 and B is a set containing the elements 3 and 4. Then it is containing the elements 1, 2, 3 and 4. Now you can see it contains all those elements which are either in A or in B or both in A and B. And the element which is common to both the sets that is 3 here once. Now next, we will discuss properties of union of sets. First property A and B, two sets then union B is equal to B union A the commutative law. Now let us see an example for this. Let A be a set containing the elements 1 and 2 and B be a set containing the elements 3 and 4. Then it contains 1, 2, 3 and 4 that containing the elements 3, 4, 1 and 2. The elements doesn't matter therefore A meaning B is equal to B union A. Now the second property is let A, B and C then union B the whole union C is equal to B union C the whole. And this is called Cative law. Now let us discuss one example 1 and 2 that containing the elements 3 and 4. And C is a set containing the elements 5 and 6. Now A union B is a set containing the elements 1, 2, E is equal to A union B which is a set containing the elements 1, 2, 3 and 4. 2 union C which is a set containing is equal to and 6. Now containing the elements 3 is equal to which is a set containing the elements 1 and 2 union B union C which is a set containing the elements is equal to the union of these two sets which is the set containing the elements 1, 2, 3. Now these two is equal therefore A union B the whole union C is equal to A union B union C the whole. The property is if A and B A union B. Now as you can see here that containing the elements 3 and 4 and A union B is a set containing the elements 1, 2, 3 and 4. Hence 1 and 2 is a subset of a set containing the elements 1, 2, 3 and 4. A union B is a subset of a set containing the elements 1, 2, B is a subset of A union B. Now the next property is set of B then A union B is equal to B. Now there will be example for this elements 1 and 2 elements 1, 2 elements 1. Now here we have taken A is a subset of B and we are getting A union B is equal to a set containing the elements 1, 2, 3 and 4 which is equal to set of B then union B is equal to B. The next property is union empty set which is noted by 5 is equal to. Now let us see one example in this let A be a set containing the elements 1 and 2 is a set with no elements. Therefore is equal to elements 1 and 2 union the empty set which is equal to a set containing the elements 1 and 2 equal to the same complement is equal to the universal set which is denoted by xi. Now let us discuss an example for this let the universal set of the elements 1, 2, 3, 4, 8, 9 and 10. The set containing the elements 1, 3. Now in complement will be the set containing the elements of universal set which are not in A. So those elements which are not in A are the complement will be the set containing the elements 2. A complement will be equal to the union of these two sets which is equal to the set containing the elements 1, 2, 3, 4, 8, 9 and 10 which is equal to the universal set. A complement is equal to the universal set. We have learnt about union of sets and its properties. This completes the session hope you all have enjoyed this session.