, b ): a , b ∈ A, b is exactly divisible by a }. Write R in roster form Find the domain of R (iii) Find the range of R. . Determine the domain and range of the relation R defined by R = {( x , x + ) : x ∈ { , , , , , }}.
. Write the relation R = {( x , x ) : x is a prime number less than } in roster form. . Let A = { x, y , z } and B = { , }.
Find the number of relations from A to B. . Let R be the relation on Z defined by R = {( a , b ): a , b ∈ Z , a – b is an integer}. Find the domain and range of R.
. Functions In this Section, we study a special type of relation called function. It is one of the most important concepts in mathematics. We can, visualise a function as a rule, which produces new elements out of some given elements.
There are many terms such as ‘map’ or ‘mapping’ used to denote a function. Definition A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, a function f is a relation from a non-empty set A to a non-empty set B such that the domain of f is A and no two distinct ordered pairs in f have the same first element. If f is a function from A to B and ( a , b ) ∈ f, then f ( a ) = b , where b is called the image of a under f and a is called the preimage of b under f .
Fig . RELATIONS AND FUNCTIONS The function f from A to B is denoted by f : A à B. Looking at the previous examples, we can easily