 Hello and welcome to the session. In this session we discussed the following question which says, if set A is equal to the set containing the elements 1, 2, 3, 4 and set B is equal to the set containing the elements 1, 4, 5, 6 Also set C is equal to the set containing the elements 4, 5, 7, 8, 9. Verify that A union B the whole union C is equal to A union B union C the whole. Before we move on to the solution, let's discuss the union of two sets A and B. This is written as A union B and this is equal to the set containing the element X such that X belongs to A or X belongs to B or X belongs to both A and B. This is the key idea that we use for this question. Let's proceed with the solution now. We are given set A equal to the set containing the elements 1, 2, 3, 4. Set B is the set containing the elements 1, 4, 5, 6 and set C is the set containing the elements 4, 5, 7, 8, 9. We need to show that A union B the whole union C is equal to A union B union C the whole. First of all, we will find A union B. Now from the key idea as you know that A union B is the set of the elements that belong to set A or set B or both the sets A and B. Now when we are supposed to find A union B so we would consider the sets A and B. Now the elements that belong to both sets A and B would be given by 1, 2, 3, 4, 5 and 6. So A union B is the set containing the elements 1, 2, 3, 4, 5 and 6. Now next we will find out B union C. B union C is the set containing the elements that belong to set B or set C or both set B and C. Now for this, let us consider the sets B and C. Now the elements that belong to both sets B and C are given as 1, 4, 5, 6, 7, 8, 9. So we have got the set B union C. Now we will find the union of A union B with C. So this would be equal to the set containing the elements that belong to the set A union B and C. So A union B the whole union C is equal to the set containing the elements 1, 2, 3, 4, 5, 6, 7, 8, 9. Let this be result 1. Now next we would find out the union of A with B union C. This would be the set containing the elements that belong to both sets A and B union C. So when we observe the two sets A and B union C we find that the elements of the set A union B union C the whole would be given by 1, 2, 3, 4, 5, 6, 7, 8 and 9. Let this be result 2. Now from the results 1 and 2 we find that A union B the whole union C that is this is equal to A union B union C the whole that is this. So hence verified this completes the session. Hope you have understood the solution of this question.