 Hello and welcome to the session it is because the following problem today given a non-empty set x consider p of x which is a set of all subsets of x defined the relation r in p of x as follows for subsets a b in p of x a r b if and only if a is contained in b is r in equivalence relation on p of x justify your answer let us write the solution r is a relation in p of x where p of x is equal to set of all subsets of x p of x is defined as a r b if and only if a is contained in b for a b subsets of x now to check r is an equivalence or not just let us check for reflexivity which implies a is contained in a which is true is reflexive now let us check for transitivity a r b which implies a is contained in b b r c which implies b is contained in c which implies a is contained in b and b is contained in c which implies a is contained in c which is true and which implies a r c r is transitive let us check for symmetry which implies a is contained in b b r a which implies b is contained in a which is not possible therefore r is not symmetric now since r is reflexive r is transitive and r is not symmetric therefore not an equivalence relation i hope you understood the problem bye and have a nice day