- #1
uncledub
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Homework Statement
f^-1(Union{Vsub alpha : alpha belongs to Lambda})=Union{f^-1(Vsub alpha): alpha belongs to Lambda}
Homework Equations
The Attempt at a Solution
Assume that x belongs to X. Then x belongs to f^-1(Union{Vsub alpha : alpha belongs to Lambda}) iff f(x) belongs to Union {Vsub alpha : alpha belongs to Lambda} iff there exists beta belongs to lambda such that f(x) belongs to Vsub beta iff there exists beta belongs to lambda such that x belongs to f^-1(Vsub beta) iff x belongs to Union{f^-1(Vsubalpha) :alpha belongs to lambda}
Isnt a proof supposed to make it so that the reader can understand it? With all of the iff's it just gets obnoxious. How does this proof work in a way that someone would actually write it?