Relations and F...

If $$A=\{2, 4\}$$ and $$B=\{3, 4, 5\}$$ then $$(A\cap B)\times (A\cup B)$$ is

$$R$$ is a relation from $$\displaystyle \left \{ 11,12,13 \right \}$$ to $$\displaystyle \left \{ 8,10,12 \right \}$$ defined by $$y=x-3$$ then the $$R^{-1}$$ .

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

If $$\displaystyle :n(A)= m, $$ then number of relations in $$A$$ are

Let $$x,y$$ be real numbers. Let $$f(x,y)= |x+y| ;\ F [f(x,y)]= -f(x,y) $$ and $$\displaystyle G [f(x,y)]= -F [f(x,y)]$$ then which of the following is true ?

If $$\displaystyle f(x) = \cos(\log x) $$ then the value of $$\displaystyle f(x)\cdot f(y)-\frac{1}{2}\left [ f\left ( \frac{x}{y} \right )+f(xy) \right ]$$ equals

If $$\displaystyle A=\left \{ 0,1,2,3,4,5 \right \}$$ and relation $$R$$ defined by $$a R b$$ such that $$2a+b=10$$ then $$ R^{-1}$$ equals

If $$\displaystyle R=\{ (x,y):x, y \in Z ,x^{2}+y^{2}\leq 4 \}$$ is a relation in $$Z$$ then domain $$D$$ is

Let $$\displaystyle A=  \left \{ a,b,c \right \} $$ and $$\displaystyle B=  \left \{ 4,5 \right \} $$ Consider a relation $$R$$ defined from set $$A$$ to set $$B$$ then $$R$$ is subset of

Let $$A$$ and $$B$$ be two finite sets having $$m$$ and $$n$$ elements respectively. Then the total number of mapping from $$A$$ to $$B$$ is