Topic 1: Mappings and Relations – Sample Activity

Context

Five friends Apio, Asiimwe, Babirye, Namono and Namuli have their first names as Babra, Cathy, Kevin, Mercy and Prisca. When they are together for a swimming game, they keep using their surnames and first names interchangeably. The sports trainer gets confused so that he cannot correctly establish both names for a person.

A Support Material

One day, somebody got information on a sheet of paper written as

• Apio went swimming with Prisca, Barbra and Cathy
• Namono travelled to Nairobi with Prisca and Cathy.
• Asimwe, Babirye, Prisca and Mercy went for a meeting in Dubai.
• Mercy, Apio and Namuli visited Asimwe
• Babirye and Cathy went shopping

Resources

Knowledge of relations and mapping

Task

Advise the sports trainer on how he can match the two names of an individual correctly.

Topic Summary

In this topic, you have learnt that:

1. a relation is a collection of ordered pairs. Relation in general defines the relationship between two different sets of information.
2. mapping denotes the relation between two sets. In mapping, the oval on the left-hand side denotes the values of domain and the oval on the right-hand side denotes the values of range.
3. the domain is the set of all input values, sometimes referred to as the object. We may describe it as the collection of the first values in the ordered pairs.
4. the range is the set of all output values, sometimes referred to as the range. We may describe it as the collection of the second values in the ordered pairs.
5. an arrow diagram consists of two oval shapes in which one shape denotes the domain of a function whereas the other oval shape denotes the range. Usually, arrows or lines are drawn between domain and range to denote the relation between two elements.
6. a one-to-one mapping is where each element of the range is paired with exactly one element of the domain.
7. a many-to-one mapping is one in which element in the range is associated with more than one element in the domain.
8. a one-to-many mapping is one in which one element in the domain is mapped with more than one element in the range.
9. a function is a special type of relation in which each element of the domain is mapped with exactly one element in the range. A one-to-one and a one-to-many describe a function.