Abstract Algebra : Mappings and Partitions
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Suppose that f is an onto mapping from A to B. Prove that if { B_lambda } , lambda is an element of the set β, is a partition of B, then { f^-1( B_lambda)}, lambda element of β, is a partition of A.
Don't get confused by the index "lambda". If it helps, you can take the partition to be B1,B2,...,Bn. The reason they have that notation is because, partitions need not be finite or even countable. However this doesn't make the problem harder.
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Solution Summary
Mappings and partitions are investigated.
Solution Preview
if {B_i : i in β} is a partition of B, we may write
B ...
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