Empty relation and Universal relation

Consider the set A= {3, 4, 5} and the number of null relations, identity relation, universal relations,reflexive relation on A are respectively n_1,n_2,n_3,n_4 ,Then the value of n_1+n_2+n_3+n_4 is equal to

Let A = {3,5}, B = {7,1}. Let R = {(a,b): ainA, binB, a-b is even}. Show that R is an universal relation from A to B.

If A={1,2,3} then which of the following relations are equivalence relation on A?

In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R

Blood Relation

Write down the relation between the universal gravitational constant G and the acceleration due to gravity at the earth's surface.

Which of one of the following relations on R is equivalence relation

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^(prime) = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Let A be the set of all students of a boys school. Show that the relation R on A given by R={(a ,\ b): a is sister of b} is empty relation and R^(prime)={(a ,\ b): the difference between the heights of a and b is less than 5 meters} is the universal relation.

Let n(A) = 6 and n(B) = p . Then , the total number of non - empty relations that can be defined from A to B is