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 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 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

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 A and B be two symmetric matrices of same order. Then show that AB-BA is a skew-symmetric matrix.

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.

Let U be the set of all triangles in a plane. If A is the set of all triangles with atleast one angle different from 60^@ , what is A' ?

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

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.