Let A and B sets. Show that `f : A xx B to Bxx A ` such that `f (a,b) = (b,a) ` is bijective function.

Let S and T be two non- empty sets. Show that, f:SxxT rarr TxxS defined by , f(a,b)=(b,a) for all (a,b) in Sxx T is a bijection.

Let A and B be two sets such that A cup B = A . Then A cap B is equal to

Let A be a finite set . If f: A rarr A is a one-one function, show that , f is a bijection.

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

Let A=RR-{2} and B=RR-{1} . Show that, the function f:A rarr B defined by f(x)=(x-3)/(x-2) is bijective .

Let f be a function defined on [a, b] such that f ′(x) gt 0, for all x in (a, b). Then prove that f is an increasing function on (a, b).

Let RR be the set of real numbers and A=R-{3},B=R-{1} . Show that , f: A rarr B defined by , f(x) =(x-1)/(x-3) is a one-one onto function.

let A={x:-(pi)/(2) le x le (pi)/(2)} and B={x:-1 le x le 1} . Show that the function f: A rarr B defined by, f(x)= sin x for all x in A , is bijective . Hence, find a formula that defines f^(-1)

If the sets A,B are such that A cup B=B cap A thrn show that A=B

Let A be a non- empty set of real numbers and f:A->A be such that f(f(x))=x AA x in R then f(x) is (A) bijection (B) one-one but not onto (C) onto but not one-one (D) neither one-one nor onto