Relations Test ...

The relation P defined from R to R as a P b $$\Leftrightarrow$$ 1 + ab > 0, for all a, b $$\epsilon$$ R is

If R is a relation on a finite set having n elements, then the number of relations on A is :

If $$A=\left\{2,3,5\right\}, B=\left\{2,5,6\right\}$$, then $$\left( A-B \right) \times \left( A\cap B \right)$$ is

If $$A=\left\{1,2,3\right\}$$ and $$B=\left\{3,8\right\},$$ then
$$\left( A\cup B \right) \times \left( A\cap B \right)$$ is

Let $$R = gS - 4$$. When $$S = 8, R = 16$$. When $$S = 10, R$$ is equal to

If the line $$x=\alpha$$ divides the area of the region $$R=\left\{(x,y)\in \mathbb{R}^2:x^3\le y\le x,0\le x\le 1\right\}$$ into two equal parts, then 

Find the domain of the function defined as $$f(x)=\dfrac{1}{1-x^2}$$.

If $$aN = (ax/x \ \epsilon \ N)$$ and $$bN \cap cN = dN,$$, where $$b, c \ \epsilon N$$ are relatively prime, then 

If $$f:R \to R$$ is a function satisfying $$f(x + y) = f(xy)$$ for all $$x, y \in R$$ and $$f\left(\dfrac{3}{4}\right) = \left( \dfrac{3}{4} \right)$$ , then $$f\left( \dfrac{9}{16} \right)$$ =