# Relations and Mappings

*Relation is an association between two objects.*- The concept of relation between two sets by finding the relation (rule of association) and drawing arrows from left hand side to right hand side.
- Mapping is an association between two sets A and B such that each element of A is associated with a unique element of B. So, "there must be an answer, and this answer should be unique".
- An ordered pair (a, b) is a pair of objects which occur in a particular order.
- Relations and mappings can also be represented by a set of ordered pairs and vice versa.
- Mappings are also called functions, usually denoted by letters f,g etc. The set of images is called range and the set of pre images is called domain of a function.
- A function may be written in roster form (set of ordered pairs) or as arrow diagram or in equation form (formula).

## Exercise

- Write true or false:

(i) An ordered pair is a pair of objects taken in any order.

(ii) (2, 3) = (3, 2)

(iii) {2, 3} = (2, 3)

(iv) If (x, 2) = (3, y) then x = 3, y = 2

(v) If (x +1, y +1) = (5, 6) then x = 4, y = 5

(vi) The relation {(0, 0), (0, 1), (0, 2)} is a mapping.

(vii) The relation {(0, 0), (1, 0), (2, 0)} is a mapping.

(viii) In a function each element has a unique image.

(ix) Domain is the set of preimages.

(x) Range is the set of images. - Consider R =

(i) Is it a mapping? If yes, write it in equation form. Hence evaluate f(5).

(ii) If f(x) = 37/6, find x.

(iii) What is the domain?

(iv) What is the range? - Consider the following arrow diagram:

(i) Is it a function? Write it in equation form.

(ii) List the elements of this function. - Given f : x
1/x where x {integral multiples of 6}

(i) What is the range of this function?

(ii) Find f(18).

(iii) If f(x) = 18, find x. - Consider the following diagram:

(i) Is it a mapping? Write in roster form.

(ii) Find the image of h.

(iii) Find the preimage of 24.

## Answers

**1.**(i) F (ii) F (iii) F (iv) T (v) T

(vi) F (vii) T (viii) T (ix) T (x) T

**2.**(i) Yes; f(x) = x +1/x; f(5) = 26/5

(ii) f(x) = 37/6 = 6 +1/6, so x = 6

(iii) Domain = {1, 2,.., 10}

(iv) Range =

**3.**(i) Yes; f(x) = x³

(ii) {(-2, -8), (-1, -1), (0, 0), (1, 1), (2, 8)}.

**4.**(i) {even integers}

(ii) 6 (iii) 54

**5.**(i) Yes; {(a, 1), (b, 2),....., (y, 25), (z, 26)}

(ii) 8 (iii) x