Relations Test ...

Let $$R$$ be a relation on $$N$$ defined by $$x+2y=8$$. The domain of $$R$$ is

Let $$A\equiv \left\{1,2,3,4\right\},\ B\equiv \left\{a,b,c\right\}$$, then number of function from $$A\rightarrow B$$, which are not onto is

If domain of $$y = f\left( x \right)$$ is $$ \left[ { - 3,\,\,2} \right]$$ then domain of $$y = f\left( {\left| {\left[ x \right]} \right|} \right)$$ is

Let  $$R = \{ ( 3,3 ) , ( 6,6 ) , ( 9,9 ) , ( 6,12 ) , ( 3,9 ) , ( 3,12 ) , ( 3,6 ) \}$$  be a relation on the set  $$A=\{ 3,6,9,12\} .$$  Then the relation  $$R ^ { - 1 }$$  is

Consider the following relations :-
$$R=\{ (x,y):x,y$$  are real numbers and  $$x =w y$$  for some rational number  $$w \}$$ :
$$S = \{ \left( \dfrac { m } { n } , \dfrac { p } { q } \right) : m , n , p$$  and  $$q$$  are integers such that   $${ n },{ q } \neq 0$$  and  $${ qm }={ pn }\}.$$   Then :

If $$A=\left\{1,2,3\right\}$$, the number of symmetric relation in $$A$$ is

If $$A=\left\{ 2,3,5 \right\} ,B=\left\{ 4,6,8 \right\} $$, then the relation from $$A$$ into $$B$$ is 

If A= {a, b} then possible number of relation on the set A.

If n(A)=4, n(B)=3, $$n(A\times B\times C)=24,then\quad n(C)$$ is equal to 

If a set $$A$$ has $$n$$ elements then the number of relations defined on $$A$$ is