The inverse of f is the relation f1:B|A defined as follows:

  • Viewing relations from B to A as subsets of B×A, we define

    f1=def{(b,f1(b))B×A | aA},

    where

    f1(b)=def{aA | f(a)=b}

    for each bB.

  • Viewing relations from B to A as functions B×A{true,false}, we define

    f1(b,a)=def{trueif there exists aA with f(a)=b,falseotherwise

    for each (b,a)B×A;

  • Viewing relations from B to A as functions BP(A), we define

    f1(b)=def{aA | f(a)=b}

    for each bB.


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