Relations Test ...

The domain of $$\dfrac { 10 ^ { x } + 10 ^ { - x } } { 10 ^ { x } - 10 ^ { - x } }$$ is

If  $$f:R\rightarrow R,g:R\rightarrow R$$ are defined by $$f(x)=5x-3,g(x)={ x }^{ 2 }+3,$$ then $$(go{ f }^{ -1 })(3)=\\ $$

If $$R$$ is the relation from set $$A$$ to a set $$B$$ and $$S$$ is the relation from $$B$$ to a set $$C$$, then the relation $$SoR$$

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by :$$(x,y)\in\;R\; \rightarrow x$$ is relatively prime to y. Then, domain of R is

If $$A$$ and $$B$$ are independent event such that $$P(A \cap B')=\dfrac {3}{25}$$ and $$P(A' \cap B)=\dfrac {8}{25}$$, then $$P(A)=$$

The relation $$R$$ on the set $$Z$$ of all integer numbers defined by $$(x,y)\ \epsilon \ R\ \Leftrightarrow x-y$$ is divisible by $$n$$ is

The relation $$“$$is congruent to$$"$$ on the set of all triangles in a plane is

The number of equivalence relations on a five element set is

Let $$A = \left\{ {1,2,3} \right\}$$ and $$R = \left\{ {\left( {1,1} \right),\left( {1,3} \right),\left( {3,1} \right),\left( {2,2} \right),\left( {2,1} \right),\left( {3,3} \right)} \right\}$$, then the relation $$R$$ and $$A$$ is

Let $$S=\{x \in R : x\geq 0$$ and $$2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}$$. Then S?