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30 MATHEMATICS 2. Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4; x, y ∈N}. Depict this relationship using roster form. Write down the domain and the range. 3. A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form. 4. The Fig2.7 shows a relationship between the sets P and Q. Write this relation (i)inset-builderform(ii)rosterform. What is its domain and range? 5. Let A = {1, 2, 3, 4, 6}. Let R be the relation onAdefined by Fig 2.7 {(a, b): a , ∈ A, b is exactly divisible by a}. (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R. 6. Determine the domain and range of the relation R defined by R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}. 3 7. Write the relation R = {(x, x ) : is a prime number less than 10} in roster form. 8. Let A = {x, y, z} and B = {1, 2}. Find the number of relations fromA to B. 9. 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. 2.4 Functions In this Section, we study a special type of relation calledfunction. It is one of the most importantconceptsinmathematics.Wecan,visualiseafunctionasarule,whichproduces new elements out of some given elements. There are many terms such as ‘map’ or ‘mapping’ used to denote a function. Definition 5 A relation f from a set A to a set B is said to be a function if every element of set Ahas one and only one image in set B. In other words, a function f is a relation from a non-empty setAto 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 fromA 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. Reprint 2026-27