 Hello and welcome to the session. Let us understand the following problem today. Let a is equal to 1, 2, 3, then number of equivalence relations containing 1, 2 is a1, b2, c3, d4. Now let us write the solution. The smallest equivalence relation containing 1, 2 is r1 given by 1, 1, 2, 3, 3, 1, 2 and 2, 1. Now equivalence relation which implies r1 is symmetric. 1, 2 belongs to r1 which implies 2, 1 belongs to r1. Now r1 is transitive also. We are left with 4 ordered pairs that is 2, 3, 3, 2, 1, 3 and 3, 1. If we add say 3, 3 to r1 then we must add 3, 2 also since it is symmetric. Then for transitivity 1, 3 and 3, 1 also. The equivalence relation r1 is the universal relation is equal to 1, 1, 2, 2, 3, 3, 1, 2, 2, 1, 3, 2, 2, 3, 1, 3 and 3, 1. The final number of equivalence relation 1, 2 is 2. Therefore the required answer is b. I hope you understood the problem. Bye and have a nice day.