Let S be the set of all strings of 0’s and 1’s, and define as follows: For every ,
Whether is one-to-one or not.
Consider be the set of all strings of , and is defined as follows:
For all the number of in minus the number of .
In one-to-one function, distinct elements in domain are mapped with distinct elements in codomain.
Objective is to determine that is one-to-one or not.
Claim: is not one to one.
For this consider the counter example in which
Whether is onto or not.
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