Check all statements that are correct. For every function, every element of the
ID: 3197393 • Letter: C
Question
Check all statements that are correct.
For every function, every element of the codomain is the image of some element in the domain.
You prove that a function is surjective by showing that every input has a corresponding output.
The range of a function is always a subset of its codomain.
You can force any function to become surjective by restricting its domain.
To prove that a function is injective, we show that if a=b, then f(a)=f(b).
It is not possible to have an onto function from a set to its own power set.
Increasing functions do not have to be strictly increasing.
Explanation / Answer
1)NO.
For every function, every element of the codomain need not to be the image of some element in the domain. Because Function can be any mapping as not mentioned which type of function.
2)YES
Surjection is when every element of codomain is mapped with atleast one element in the domain.
3)YES
The range is the subset of the codomain. Codomain is the set of values that could possibly come out. Range lies with in the codomain.
4)NO
By restricting the domain we cannot force the function to be surjective.
5)NO
First if f(a)=f(b) then a=b. that is injective function.
6)YES
It is not possible to have an onto function from a set to its own power set according to cantors theorem.
7)YES
Increasing functions do not have to be strictly increasing. Only strictly increasing functions have to be strictly increasing.