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    Hi everyone,

    Would appreciate help on some of these questions, in particular questions 3, first of all i believe that it is a bijection, agree? I am currently working on the assumption that it is but struggling to the the first part.

    Any suggestions, worked examples etc. would be greatly appreciated, really just looking for any sort of help

    Thanks in advance
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    (Original post by betapro)
    Hi everyone,

    Would appreciate help on some of these questions, in particular questions 3, first of all i believe that it is a bijection, agree? I am currently working on the assumption that it is but struggling to the the first part.

    Any suggestions, worked examples etc. would be greatly appreciated, really just looking for any sort of help

    Thanks in advance
    To show that is a bijection, you need to show that F(a,b) is one-one and onto i.e. that:

    a) F(a,b) = F(c,d) \Rightarrow (a,b)=(c,d)
    b) for all (p,q) \in Y \times Y, there is an (a,b) \in X \times X with F(a,b) = (p,q)

    Hints:

    For a), what is the definition of the equivalence of ordered pairs?
    For b), bijective functions have inverses.
 
 
 
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