 Hello and welcome to this session. In this session we will learn about intersection of sets and its properties. First of all let us discuss intersection of sets. Now the intersection of two sets A and B is a set that contains that is the set A and set B that is A intersection B which is used for the intersection so A intersection B is equal to the set containing the element X such that X belongs to A that means A intersection B is the set of all those elements that are in A and B. But for example here if A is a set containing the letters and B is a set containing the letters that are the letters of the word book. So A is a set containing the elements B. B is a set containing the letters of the word book. So B is a set containing the elements C. Now A is a set containing B is a set and B both. So here the elements which are in A and B both are section B is a set containing the elements the properties of intersection of sets. Now if A and B are the first property of intersection of sets is section B is equal to B intersection A the commutative law. Now let us discuss one example to prove this property. Now we are let A is a set containing the elements A, E and B is a set containing the elements B, C, D and now A is equal to section B is a set containing the elements which are in A and B both. Now here this is the set A and this is the set B and the elements which are in common to both these set section B is a set containing the elements B intersection A. Now B intersection A is a set containing the elements which are in B and A both. This is the set A and this is the set B and common which are in B and A both. So B intersection A is a set containing. Now these two therefore E is equal to B intersection is second property of the intersection of sets and that is if A, B and C are three sets then A intersection B the whole intersection C is equal to A intersection B intersection C the whole and this is common. Now for proven use let us discuss now we are let the set A is a set containing the elements and U and B is a set containing the elements A, B, C, D and E intersection B will be equal to the set containing the elements which are in A and B both and those elements section B is equal to the set containing the elements A and E, B intersection C which are in B and C both. Now A in common to the set B and C so B intersection let us find A intersection B double intersection C. Now A intersection B is a set containing the elements A and E which is a set containing the elements E. Now we have to find the intersection of these two sets will be equal to the set containing B intersection C the whole. Now A is a set containing the elements A and U intersection B intersections. Now we have to find the intersection of these two sets the single element E is only one element which is E is common to both the sets. Subsection B the whole intersection C is equal to C the whole which is called the associative law. Now let us discuss the next property which is subset of B that is the set A is a subset of set B then the section B is equal to A and here let A and 3 and B is a set containing the elements 1, 2, 3, 4 and 5. Now here you can see that A is a subset of B set of B and now will be equal to the set 1, 2. Now you can see that the set containing the elements 1, 2 and 3 is equal to the set is equal to the set of B then section B is equal to the set A. This is the next property which is intersection B is a subset of set A. Now let us discuss one example now here E, I, O and U and B is a set containing the elements A, B, C, D and E then section B will be equal to the set containing the element E that is the set A intersection B that A intersection B is a subset of the set A. So we can write A intersection B is a subset of the set B. Now let us discuss the next property intersection the empty set which is 5. Now let us discuss one example and here let the set A is a set that is the set with no elements. Then A intersection 5 will be equal to the set containing the elements which are in A that are the elements which are common to both these sets. But here you can see that there is no element which is in common to both these sets. Therefore A intersection 5 is a set with no elements which is denoted by the next property which is the subset of the universal set that the universal set is denoted by xi then A intersection A complement is equal to xi which is the Now let us discuss one example. Now here if the universal set xi is a set containing the elements 1, 2, 3, 4, 3 and 4 of the universal set which are not in A complement is a set containing the elements 1, element will be equal to now A is a set containing the elements 2, 3 and 4. Now we have to find the intersection that means we have to find the element both. Here we can observe that there are no elements which are in A and A complement both that is there are no elements which are in common to both these sets. This means that A intersection A complement is an empty set of the universal set when A intersection A complement is an empty set. We have learnt about it