Relations Test ...

Let A and B be two sets such that $$A\times B=\left\{ \left( a,1 \right) ,\left( b,3 \right) ,\left( a,3 \right) ,\left( b,1 \right) ,\left( a,2 \right) ,\left( b,2 \right)  \right\} ,$$ then 

A relation R is defined from {2,3,4,5} to {3,6,7,10} by XRY $$\Leftrightarrow $$ X is relatively prime to Y, then domain of R is 

If the cardinality of a set $$A$$ is $$4$$ and that of a set $$B$$ is $$3$$, then what is the cardinality of the set $$A\Delta B$$.

What type of a relation is "Less than" in the set of real numbers?

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

Let $$A$$ be set of first ten natural numbers and $$R$$ be a relation on A, defined by $$(x,y)\in R\Rightarrow x+2y=10$$, then domain of $$R$$ is 

Let $$S=\{1, 2, 3, 4, 5\}$$ and let A$$=S\times S$$. Defined the relation on the R on A as follows (a, b)R(c, d) if an only if ad$$=$$bc. Then R is?

Let $$g(x)-f(x)=1$$. If $$f(x)+f(1-x)=2\forall x\in R$$, then $$g(x)$$ of symmetrical about?

A is a set having $$6$$ distinct elements. The number of distinct function from A to A which are not bijections is?

N is the set of natural numbers. The relation R is defined on the N$$\times$$N as follows $$_{a\cdot b}R_{c\cdot d}\Leftrightarrow a+d=b+c$$. Then, R is?