Explanation:

Given set {(x,y)|x y = 5}

To understand the properties of this set, we need to convert it into a function.

A function is a relation between two sets, where each element of the first set is related to exactly one element of the second set.

Let's consider the set {(x,y)|x y = 5} as a relation between two sets X and Y.

X = {x| x is a real number}

Y = {y| y is a real number}

Now, let's check whether this relation is a function or not.

To be a function, each element of set X should be related to exactly one element of set Y.

If we take x = 1, then y can be either 5 or 1/5. Hence, x is related to two elements of set Y, which violates the definition of a function.

Therefore, the given set {(x,y)|x y = 5} is not a function.

But, it can be converted into a one-to-one mapping.

One-to-One Mapping:

A one-to-one mapping is a function where each element of set X is related to one and only one element of set Y.

To make the given set {(x,y)|x y = 5} a one-to-one mapping, we need to restrict the domain and range of the sets X and Y.

Let's restrict X to {x| x > 0} and Y to {y| y > 0}.

Now, if we take any element x from X, it will be related to only one element y from Y, and vice versa.

Hence, the given set {(x,y)|x y = 5} is a one-to-one mapping.