Question

Let D = {x| x is a student} be the domain, and let ƒ(x) = “date of birth” be the possible function. Determine if the relation is an example of a function. Yes, ƒ is a function. No, ƒ is not a function.

Answer 1

Remember that a function is a special type of relation in which each element of the domain is paired with only one element in the range; in other words for each $D$ value, there is only a $f(x)$ value.

Since D = {x| x is a student}, the domain of the relation is the set of all students; on the other hand, ƒ(x) = “date of birth”, so the range of the relation is the set of the birth dates of the students. Since in a room of 23 people there is a 50% chance of two people sharing the same date of birth, it is inevitable that in the set of all the students there is at least two students that share the same date of bird; therefore two elements in the domain will be paired with the same element in the range. Given that, We can conclude that the relation is not a function.