# Lecture - 2 Chapter 2 Relations and Functions

You must expect great things of yourself before you can do them. —Michael Jordan

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

NCERT EXERCISE 2.2 |

**Question 1.** Let A = {1, 2, 3,…,14}. Define a relation R from A to A by R = {(*x*, *y*) : 3*x* – *y* = 0, where *x*, *y* ∈ A}. Write down its domain, co-domain and range.

**Question 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.

**Question 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.

**Question 4.** The Fig 2.7 shows a relationship between the sets P and Q. Write this relation**(i)** in set-builder form **(ii)** roster form. What is its domain and range?

##### Clip - 1

**Question 5.** Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(*a*, *b*): *a*, *b* ∈ 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.

**Question 6.** Determine the domain and range of the relation R defined by R = {(*x*, *x* + 5) : *x* ∈ {0, 1, 2, 3, 4, 5}}.

**Question 7.** Write the relation R = {(*x*, *x*^{3}) : *x* is a prime number less than 10} in roster form.

**Question 8.** Let A = {*x*, *y*, *z*} and B = {1, 2}. Find the number of relations from A to B.

**Question 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.