S.2 MATHEMATICS LESSON TWO :TYPES OF MAPPING
Mappings and relations are concepts in mathematics that involve the relationship between two sets or groups of elements.
A mapping, also known as a function, is a relation between two sets in which each element from the first set (domain) is paired with exactly one element from the second set (codomain). In other words, a mapping assigns each element of the domain to a unique element in the codomain.
For example, consider the mapping f: {1, 2, 3} -> {a, b, c}, where f(1) = a, f(2) = b, and f(3) = c. This mapping assigns each element in the domain {1, 2, 3} to a unique element in the codomain {a, b, c}.
Mappings can also be represented using tables, graphs, or algebraic expressions. They are widely used in various mathematical concepts, such as calculus, algebra, and discrete mathematics.
A relation, on the other hand, is a general concept that describes any connection or association between elements of two sets. Relations do not necessarily have to be one-to-one or onto like mappings. They can be many-to-one, one-to-many, or even many-to-many.
For example, consider the relation R = {(1, a), (1, b), (2, c), (3, a)}. This relation represents the connections between elements of the set {1, 2, 3} and the set {a, b, c}. In this case, the element 1 is related to both a and b, and hence, it is a many-to-many relation.
Relations can also be represented using tables, graphs, or algebraic expressions. They are used in various areas of mathematics, such as number theory, algebraic structures, and set theory.
In summary, mappings and relations are essential concepts in mathematics that describe the relationships between elements of two sets. Mappings, also known as functions, assign each element of the domain to a unique element in the codomain, while relations describe general connections or associations between elements of two sets, which can be one-to-one, onto, many-to-one, one-to-many, or even many-to-many.
