Relations Test ...

The total number of equivalence relations defined in the set $$S={a,b,c}$$ is 

The relation $$\bot $$ is

The minimum number of elements that must be added to the relation $$R=\{(1, 2), (2, 3)\}$$ on the set $$\{1, 2, 3\}$$ so that it is an equivalence relation.

A relation $$R_1$$ is defined set $$A={1,2,3}$$ such that $$R_1\equiv {(1,1),(2,2),(2,3),(3,2)}$$, then minimum number of elements required in $$R_1$$ so that $$R_1$$ becomes R which in an equivalence relation is

 $$R={(1, 2), (2,3),(3 4)}$$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is 

If $$\int\dfrac{2\cos x-\sin x+\lambda}{\cos x-\sin x-2}dx=A In\left|\cos x+\sin x-2\right|+Bx+C$$. Then the ordered triplet $$\left(A,B,\lambda\right)$$, is 

The maximum number of equivalence relation on the set $$A=\{1,2,3,4\}$$ are

The number of reflexive relations of a set with three elements is equal to 

Let R be a relation over set N$$\times N$$defined by (a,b)R (c,d) if a + d = b + c then R is ...... ( Here N is the set of all natural numbers)

Let $$s = \{(x, y)| \sin y = \sin x; x, y \in R \}$$, then $$s$$ is