If A function f: A →B is a one-to-one function, then*Number of elements in range of f is n(A)n(A)=n(B)Number of elements in range of f is n(B)n(A)> number of elements in range of f

The statement seems to be a bit jumbled, but I'll try to clarify the concepts involved.

A function f: A → B is said to be one-to-one (or injective) if every element in A maps to a unique element in B and no element in B is the image of more than one element in A.

1. "Number of elements in range of f is n(A)": This statement is saying that the number of elements in the range of f (the set of all outputs of the function) is equal to the number of elements in the set A. This would be true for a one-to-one function, because each element in A maps to a unique element in B.

2. "n(A) = n(B)": This statement is saying that the number of elements in set A is equal to the number of elements in set B. This is not necessarily true for a one-to-one function. A one-to-one function can have a larger set B, but not a smaller one.

3. "Number of elements in range of f is n(B)": This statement is saying that the number of elements in the range of f is equal to the number of elements in set B. This would be true for a function that is both one-to-one and onto (surjective), because every element in B is the image of some element in A.

4. "n(A) > number of elements in range of f": This statement is saying that the number of elements in set A is greater than the number of elements in the range of f. This cannot be true for a one-to-one function, because in a one-to-one function, each element in A maps to a unique element in B. So, the number of elements in the range of f cannot be less than the number of elements in A.