Let f be a subset of `ZZ xxZZ` such that `f={(xy,x-y):x, y in ZZ}` Is f a mapping from `ZZ "into" ZZ`. Give reasons for your answer.

Let ZZ be the set of integers and f be a subset of ZZxxZZ , such that, f={(xy,x +y):x,y in ZZ} Is f a function from ZZ " into "ZZ ? Give reasons for your answer.

Let ZZ be the set of integers and A={x:x =6n, n in ZZ},B={x : x =4n,n in ZZ}, find A capB.

Let ZZ be that set of integers and f:ZZ rarr ZZ be defined by f(x)=2x, for all x in ZZ and g: ZZ rarr ZZ be defined by, (for all x in ZZ) g(x)={((x)/(2) " when x is even" ),(0" when x is odd" ):} Show that, (g o f) =I_(ZZ) , but (f o g) ne I_(ZZ) .

Let ZZ be the set of integers and let R be the relation on ZZ defined as R={(x,y)|x,y in ZZ and x^2+y^2=100} Find R as the set of ordered pairs. Also find its domain and range.

Let f be a function such that f(xy)=(f(x))/y for all positive real numbers x, y. If f(20) = 15, then f(50) =

Let f be a function defined by f(xy)=(f(x))/(y), AA x, y in R^(+) .If f(30)=20 .Then f(40)=

Let f be a function such that f(xy)=(f(x))/(y) for all positive real numbers x,y .If f(20)=15, then f(50)=

Let f: ZZ->ZZ\ a n d\ g: ZZ->ZZ\ be functions defined by f={(n , n^2): n in ZZ} and g={(n ,|n|^2): n in ZZ} . Show that. f=g .