Prove or disprove (find a counterexample) : If A C B and f : A --> B is an onto function (the range of f is all of B), then f is one-to-one and A =B.
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Because, b belong to B and a belong to A,
f: A ->B <==> b = f(a)
Because, range (f) = B
Because, by ...
The discrete structures of onto and one-to-one are determined.