If R is the set of all real numbers. what do the cartesian products `R xx R` and `R xx R xx R` represent ?

If R is the set of real numbers and Q is the set of rational numbers, then what is R-Q?

Show that the function f : R_* rarr R_* defined by f (x) = 1/x is one-one and onto, where R_* is the set of all non-zero real numbers. Is the result true, if the domain R_* is replaced by N with co-domain being same as R_* ?

Let S be the set of all real numbers and let R be the relation in S defined by R = {(a,b), a leb^2 }, then

Let R be the set of real numbers. Define a real function f : R rarr R by f (x) =x + 10 . Sketch the graph of this function.

Let R be the set of all real numbers. Let f: R rarr R be a function such that : |f(x) - f(y)|^2 le |x-y|^2, AA x, y in R . Then f(x) =

Let N be the set of all natural numbers and R be a relation in N defined by : R = {(a, b) : a is a factor of b} Show that R is reflexive and transitive.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxxNdot

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Show that zero is the identity for addition on R and 1 is the identity for multiplication on R. But there is no identity element for the operations – : R xx R rarr R and -: R_* xx R_* rarr R_*

Show that the relation R in the set R of real numbers defined as R = {(a, b) : a le b} , is reflexive and transitive but not symmetric.