If and are function and is onto, must f be onto? Prove or give a counterexample.
When are two functions and is onto, then whether must be onto or not.
are two functions.
A function is said to be onto if every element in codomain is mapped with atleast one element in domain.
Let be any sets and the functions are .
Consider the composite function is onto.
The objective is to prove or provide counter example for the result must be onto.
Consider the statement, if are functions and is onto, then must be onto.
This statement is not true for all sets with the reference of the counter example.
Find the arrow diagram for functions .
From the arrow diagram of the functions the composition is onto one but the functions is not onto
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