Relations Test ...

The relation $$R$$ defined on the set $$A=\left\{ 1,2,3,4,5 \right\} $$ by $$R=\left\{ \left( a,b \right) :\left| { a }^{ 2 }-{ b }^{ 2 } \right| <16 \right\} $$, is not given by

If $$R$$ is a relation on the set $$A=\left\{ 1,2,3,4,5,6,7,8,9 \right\} $$ given by $$xRy\Leftrightarrow y=3x$$, then $$R=$$

Let $$A=\left\{ 2,3,4,5,....,17,18 \right\} $$. Let $$\simeq $$ be the equivalence relation on $$A\times A$$, cartesian product of $$A$$ with itself, defined by $$(a,b)\simeq (c,d)$$, iff $$ad=bc$$. The the number of ordered pairs of the equivalence class of $$(3,2)$$ is

If $$R$$ is the largest equivalence relation on a set $$A$$ and $$S$$ is any relation on $$A$$, then

The maximum number of equivalence relations on the set $$A=\left\{ 1,2,3 \right\} $$ is

For real number $$x$$ and $$y$$, define $$xRy$$ iff $$x-y+\sqrt{2}$$ is an irrational number. Then the relation $$R$$ is

If $$A=\left\{ a,b,c,d \right\} $$, then a relation $$R=\left\{ \left( a,b \right) ,\left( b,a \right) ,\left( a,a \right)  \right\} $$ on $$A$$ is

The number of ordered pairs (a, b) of positive integers such that $$\dfrac{2a - 1}{b}$$ and $$\dfrac{2b - 1}{a}$$ are both integers is 

Let Z be the set of all integers and let R be a relation on Z defined by $$a$$ R $$b\Leftrightarrow (a-b)$$ is divisible by $$3$$. Then, R is?

If $$A=\{2, 4, 5\}, B=\{7, 8, 9\}$$ then $$n(A\times B)$$ is equal to