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


Question 1. Let A = {1, 2, 3,…,14}. Define a relation R from A to A by R = {(x, y) : 3xy = 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, yN}. 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?

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, x3) : 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, ab is an integer}. Find the domain and range of R.