Show that `f:N rarr N` given by
`f(x)={{:(x+1", if x is odd"),(x-1", if x is even"):}`
is both one-one and onto.

Show that f : NrarrN , given by : f(x) = {(x+1,,if x is odd,,),(x-1,,if x is even,,):} is both one-one and onto.

Show that f : N to N , given by f(x)= {(x+1", if x is odd"),(x-1", if x is even"):} is bijective (both one-one and onto).

Show that f:Nto N, given by f (x) = x + 1 , if x is odd, f (x) = x -1, if x is even is both one-one and onto.

Show that f : NvecN , given by f(x)={x+, if x i s od dx-1, if x i s e v e n is both one-one and onto.

Show that f:Nto N, given by x + 1, if x is odd, f (x) = x -1, if x is even is both one-one and onto.

Show that f:Nto N, given by x + 1, if x is odd, f (x) = x -1, if x is even is both one-one and onto.

Show that f:Nto N, given by x + 1, if x is odd, f (x) = x -1, if x is even is both one-one and onto.

Show that f\ : NvecN ,\ given by f(x)={x+1, if\ x\ i s\ od d \ \ x-1,\ \ if\ x\ i s\ e v e n is both one-one and onto.

Let NN be the set of natural numbers: show that the mapping f NN rarr NN given by, f(x)={(((x)+1)/(2) "when x is odd" ),((x)/(2)" when x is even"):} is many -one onto.