1. Let {a,b,c}{1,2,3and {P,Q,R,S}. Classify the following three functions as injective, surjective, bijective, or none of these:

    · f:Xgiven by f(a)=cf(b)=and f(c)=c
    · g:given by g(1)=bg(2)=and g(3)=c
    · h:Xgiven by h(a)=Ph(b)=and h(c)=Q

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1 Answer

Function f: X to itself omits b as an output (permissible as an injective function), but c has more than one input (cannot be injective). Cannot be surjective (but b is omitted). f is not a function—none.

Function g: the inputs and outputs form perfect pairs with nothing left out (the sets are the same size). Bijective.

Function h: R is omitted as an output and other mapping is unique—injective.

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