Let S be the set of all sets and let `R={(A,B):AsubsetB}` i.e A is a proper subset of B.Show that R is (i).Transitive

Let S be the set of all sets and let R={(A,B):AsubsetB} i.e A is a proper subset of B.Show that R is not symmetric

Let S be the set of all sets and let R={(A,B):AsubsetB} i.e A is a proper subset of B.Show that R is Not reflexive

Let T be the set of all triangles in a plane with R a relation in T given by {(T_1,T_2):T_1~=T_2} show that R is an equivalence relation.

Let X and Y be two non-empty sets such that XnnA=YnnA=phiandXuuA=YuuA for some non-empty set A. Then, a)X is a proper subset of Y b)Y is a proper subset of X c)X = Y d)X and Y are disjoint sets

Show that the relation R in the set R of Real numbers defined as R={(a,b):aleb^2} is neither reflexive, nor symmetric, nor transitive.

Let A be the set of all students of a boys school. Show that the relation R in A given by R ={(a, b): a is sister of b} is the empty relation and R' ={(a, b): the difference between heights of a and b is less than 3 meters} is the universal relation.

Let R be the set of all real numbers and let f:R rarr R be a function defined by f(x) = x +1 Draw the graph f

Let P be the set of all subsets of a given set X. Show that uu: P xx P rarr P given by (A, B) rarr A uu B and nn: P xx P rarr P given by (A, B) rarr A nn B are binary operations on the set P .

Let A={1,2,3,4,6} .Let R be the relation on A defined by R={(a,b):a,b in A, b is exactly divisible by a} Write R in roster form.