Question

cite a real-world example or scenario that can be expressed as a relation that is not a function​

Answer 1

Step-by-step explanation:

A relation is a subset of the cartesian product V x W, so a set of tuples {(v1, w1), (v2, w2), …} with each v[i] an element of V and each w[i] an element of W.

The sets V and W can be finit, countable infinite (like the set of natural numbers) or uncountable infinite (like the set R of real numbers).

A few examples:

Let V be the set of all people and W be the set of all cars. Then we can make a Venn diagram with arrows starting in V and ending in W that express ownership. A person can own 0, 1, 2, … cars. So this is not a function.

Answer 2

The Set of parents with their children is a  real life example which is relation but not a function.

Step-by-step explanation:

• Relation between two sets is the relationship between elements of two sets which are expressed in an ordered pair (x,y) where the first elements of the pairs are called the domain (x-values) and the second are called the range (y-values).
• We know, A Function is a relation from a set of inputs (domain) to a set of possible outputs (range) where, each input can have only one output.
• The real life scenario is - The relation of a parent to a child, though it can be a relation but it cannot be function. Here the set of parent can be considered as the input (domain) and the set of their children can be considered as the output (range). It should be noted that:
• It is not necessary that all parents have children. Therefore, the first condition to be a function is not fulfilled wherein each input should have an output.
• Also, It is not necessary that all parents have only one child. In many cases, people have 2 to 3 children. Therefore, the second condition of being a function wherein each input can have only one output is also not fulfilled.

Hence, the set of parents with their children is a relation but not a function.