Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.

Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=(b ,\ a) is a bijection.

Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=(b ,\ a) is a bijection.

Let A = R - (-5) and B = R . Let the function f: A to B be defined as f(x) = (5x + 4)/( x + 5) , x in A . Show that f is an injective function.

Let A , B and C be the sets such that A uu B=A uu C and A nn B = A nn C . show that B=C

Let A , B and C be the sets such that A uu B=A uu C and A nn B = A nn C . show that B=C

Let f : A to B and g : B to C be the bijective functions. Then (g of )^(-1) is

Let A and B be any two sets such that n(B)=P, n(A)=q then the total number of functions f: A -> B is equal to

Let A and B be any two sets such that n(B)=P, n(A)=q then the total number of functions f: A -> B is equal to

Let Z be the set of integers. Show that the relation R={(a ,\ b): a ,\ b in Z and a+b is even} is an equivalence relation on Zdot

Show that the function f: Rvec given by f(x)=x a+b , where a , b in R ,a!=0 is a bijection.