 Hi and how are you all today? I am Priyanka and let us discuss the question. It says let A is equal to having elements 1, 2, B is equal to 1, 2, 3, 4, C is equal to 5, 6 and D is equal to 5, 6, 7, 8. Verify that for the first part A cross B intersection C is equal to A cross B intersection A cross C. Second part A cross C is a subset of B cross D. Right, let us start with our solution. Let us write down the sets given to us one again. For the first part we need to find out A cross B intersection C. We need to verify A cross B intersection C is equal to A cross B intersection A cross C. Let us divide into two columns. This be the left hand side and this be the right hand side. A cross B intersection C and here A cross B intersection A cross C. First of all, what is the value of B intersection C? Is there any element common to B and C? The answer is 5. So, what will be B intersection A cross 5? That will be the answer as 5. Proceeding on to our left hand side, right hand side. First we need to have A cross B that will be ordered pairs 1, 1, 1, 2, 1, 3, 3, 1, 4, 2, 1, 2, 2, 2, 3, 2, 4. Right, proceeding on. Now here A cross C will be having elements as 1, 5, 1, 6, 2, 5 with 2, 6, right. Now is there any term which is common to both these sets? Because in the middle we have intersection and the answer comes out to be a null set. So, LHS is equal to RHS and hence we can write that it is verified. This completes the first part. Proceeding on to the next part. Here we need to verify that is A cross C is a subset of B cross T. Now let us first find out A cross C. It would be 1 paired with 5, 1 paired with 6, 2 paired with 5 and 2 paired with 6 which we found out in earlier part also. Now we need to find out B cross T also and this will be a little bigger 1. 1 paired with 5, 1 paired with 6, 1 with 7, 1 with 8. Similarly 2 with 5, 2 with 6, 2 with 7 and 2 with 8. Proceeding on 3 with 5, 3 with 6, 3 with 7, 3 with 8, 4 with 5, right. Now, so we need to think for being a subset all the elements of A cross C should be present in the elements of B cross T. So, let us see. This is right, this is present, this is present and this is present. So, all the elements of A cross C are present in B cross T. So, we can write A cross C is a subset of B cross T. So, this we have verified also and this brings to us to the end of this session. So, I hope you enjoyed this session and now know how will you have the ordered pair set. Bye for now.