Let A and B be sets.Show that `f:A times B rarr B times A `such that (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.

If f:A rarr B,g:B rarr C are bijective functions show that gof:A rarr C is also a bijective function.

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

Show : A times ( B - C ) = ( A times B ) - ( A times C )

Theorem 10(Let A and B be non empty set such that A xx B=A xx C. Show that B=C

Show that quad *:R xx R rarr R given by (a,b)rarr a+4b^(2) is a binary operation.

Let Z be the set of integers and f:Z rarr Z is a bijective function then

Show : ( a/b times c/d ) = ( a times c )/ ( b times d )

If A and B are two sets such that A xx B = phi , then which of the following must be true ?

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