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Q: Is it true in a relation for each element of the domain there is only one corresponding element in the range?

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A relation is a mapping between two sets, a domain and a range. A function is a relationship which allocates, to each element of the domain, exactly one element of the range although several elements of the domain may be mapped to the same element in the range.

It is an injective relation.

Function

All functions are relations with the condition that each element of the domain is paired with only one element of the range. A relation is any pairing of numbers from the domain to the range.

The domain of the inverse of a relation is the range of the relation. Similarly, the range of the inverse of a relation is the domain of the relation.

A relation where each element of the domain is paired with only one element of the range is a one to one function. A one to one function may also be an onto function if all elements of the range are paired.

It is an invertible function.

Not every relation is a function. A function is type of relation in which every element of its domain maps to only one element in the range. However, every function is a relation.

Consider the mapping between two sets, A and B. To each element of A is associated a unique element from the set B. The elements of set A which are mapped (the inputs) comprise the domain. The corresponding elements from set B comprise the range.

When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").

It is the set on which the relation is defined to the set which is known as the range.

For every element on the domain, the relationship must allocate a unique element in the codomain (range). Many elements in the domain can be mapped to the same element in the codomain but not the other way around. Such a relationship is a function.

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