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Consider the function f:A→A defined by f(x)=x+1 and justify your answers.
a) For A=Ν (integers) is f onto?

b) For A=R(real number) is f injective?

c) For A=Q (rationals) is f onto?

d) For A=Z(all integers) is f a bijection?

Solution Preview

a) No. There is no such element in the domain whose image is 1 in the codomain. Note that 0 is ...