If A = {1,3,5} and B = {2,3} then
(i) find A x B and B x A
(ii) Is A x B = B x A? If not why?
(iii) Show that n(A x B) = n(B x A) = n(A) x n(B)

If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

Let A = {1,2,3} and B = {x| x is a prime number less than 10}. Find A x B and B x A.

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R₁ = {(3,7), (4,7), (7,10), (8,1)}

The arrow diagram shows a relationship between the sets P and Q. Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R.

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, which of the following are relation from A to B ?
R₁ = {(2, 1), (7,1)}

Let A = {1, 2, 3, 4,..., 45} and R be the relation defined as ''is square of a number” on A. Write R as a subset of A x A. Also, find the domain and range of R.

A Relation R is given by the set {(x, y) / y = x + 3, x \(\in \) {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

Let X = {1, 2, 3, 4} and Y = {2, 4, 6, 8,10} and R = {(1, 2),(2, 4),(3, 6),(4, 8)} Show that R is a function and find its domain, co-domain and range?

A relation ‘f’ \(X \rightarrow Y\) is defined by f(x) = x² - 2 where x \(\in \) {-2, -1, 0, 3} and Y = R
(i) List the elements of f
(ii) Is f a function?

If X = {–5, 1, 3, 4} and Y = {a, b, c}, then which of the following relations are functions from X to Y ?
R₁= {(–5, a), (1, a), (3, b)}

Let f{(x, y)| x, y \(\in \) N and y = 2x}. be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?

Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x \(\in \) X, f(x) = x² + 1}. is a function from X to N?

Let f(x) = 2x + 5. If x ≠ 0 then find \(\frac { f(x+2)-f(2) }{ x } \).

A function f is defined by f(x) = 3 - 2x. Find x such that f(x²) = (f(x))².