Relations Test ...

If two sets $$A$$ and $$B$$ have $$ 99$$ elements in common, then the number of elements common to each of the sets $$A \times B$$ and $$B \times A$$ are

Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is

If $$A=\left \{ 1,2,3 \right \} $$ and $$B=\left \{ 4,5,6 \right \}$$ then which of the following sets are relation from $$A$$ to $$B$$
(i) $$\displaystyle R_{1}=\left \{ (4,2) (2,6)(5,1)(2,4)\right \}$$
(ii) $$\displaystyle R_{2}=\left \{ (1,4) (1,5)(3,6)(2,6) (3,4)\right \}$$
(iii) $$\displaystyle R_{3}=\left \{ (1,5) (2,4)(3,6)\right \}$$
(iv) $$\displaystyle R_{4}=\left \{ (1,4) (1,5)(1,6)\right \}$$

If n | m means that n is a factor of m, the relation | is

The relation R {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A {1, 2, 3} is

The relation "is subset of" on the power set P(A) of a set A is

The minimum number of elements that must be added to the relation R {(1, 2), (2, )} on the set of natural numbers so that it is an equivalence is

Let $$R_1$$ and $$R_2$$ be equivalence relations on a set A, then $$R_1 \cup R_2$$ may or may not be

Let N denote the set of all natural numbers and R a relation on N $$\times$$ N. Which of the following is an equivalence relation?

Let A and B be finite sets containing m and n elements respectively. The number of relations that can be defined from A to B is