Relations and F...

$$A$$ and $$B$$ are two sets having $$3$$ and $$4$$ elements respectively and having $$2$$ elements in common. The number of relations which can be defined from $$A$$ to $$B$$ is

A function $$f : R \rightarrow  R$$ satisfies the equation $$f(x)f(y) -  f(xy) = x + y$$ for all $$x, y \in R $$ and $$f(1) > 0$$ then

If $$R$$ is a relation from a finite set $$A$$ having $$m$$ elements to a finite set $$B$$ having $$n$$ elements, then the number of relations from $$A$$ to $$B$$ is:

The relation $$R$$ is defined in $$A = \left\{1,2,3\right\}$$ by $$a\ R$$ $$b$$ if $$|a^2 - b^2| \le 5$$. Which of the following is false?

If $$A = \{1, 2 \}$$ and $$B = \{3, 4\}$$ then find $$A \times B$$

If $$R = \{(x, y):3x + 2y = 15 \text{ and }x\,, y\,\in \, N\}$$, the range of the relation R is .........

If $$h(x)=x^2-2$$, then the value of $$\displaystyle\frac{1}{2}h\left(\frac{1}{2}\right)$$ is

If f is an identity function then f(-5) = __________

The domain of the relation R = $$\displaystyle \left \{ \left ( x,y \right ):x,y\epsilon N \ and\ x+y\leq 3 \right \}$$ is____

If $$(3p+q,p-q)=(p-q,3p+q)$$, then: