If the set A has m elements, B has n elements then the number of elements in A x B is ______.

Let R be a relation from a set A to B, then ______.

If R is a relation from a finite set A having m elements to a finite set B having n elemen.ts, then the number of relations from A to B is ______.

Which one of the following is not a function

Let f(x) = Ix-1I then ______.

Let \(f\) and  \(g\) be real functions defines by \(f(x)=\sqrt { x+2 } \)  and  \(g\) ,then\(g(x)=\sqrt { 4-{ x }^{ 2 } } \) find the following function: f . g

Let \(f\) and  \(g\) be real functions defines by \(f(x)=\sqrt { x+2 } \)  and  \(g\), then\(g(x)=\sqrt { 4-{ x }^{ 2 } } \) find the following function: \(\frac { f }{ g } \)

If U = {1,2,3,4} and R = {(x,y) : y > x for all, x, \(y\in U\)}, then find domain and range of R.

Find the domain and range of the relation R = {(x, y) : x + y = 8; x, \(y\in N\)}

Let\(f:\left[ 2,\infty \right] \rightarrow R\) and \(g:\left[ -2,\infty \right] \rightarrow R\)  be two real functions defined by \(f(x)=\sqrt { x-2 } \) and \(g(x)=\sqrt { x+2 } \). Find \(f+g\) and \(f-g\)

Find the values of x and y if (x + 4, x + 2y) = (6, 8)

Find the values of x and y if ( x³-x, y² - 5y + 6) = (0, 0)

If A = {1, 2, 3}, B = {3, 4} and C = {1, 3, 5}, find (A x B) \(\cap\) (A x C)

If A = {1, 2, 3}, B = {3, 4} and C = {1, 3, 5}, find A x (B \(\cup\) C)

If A = {1, 2, 3}, B = {3, 4} and C = {1, 3, 5}, find  A x (B \(\cap\) C)

Find the values of a and b, if (a-3,b+7)=(3,7)

Which of the following relations are functions?
\( \left\{ (3,3),(4,2),(5,1),(6,0),(7,7) \right\} \)

Which of the following relations are functions?
\(\left\{ (2,0),(4,8),(2,1),(3,6) \right\} \)

Find the cartesian product of three sets A = {1,2}, B = {3,4} and C = { x : x \(\in \) N and 4 \(\le \) x \(\le \)6}.

Let A = {a,b,c} and B={x: x\( \in \) N, x is a prime number  less than 5}. Find A x B ans B x A.
Show that A x B \( \neq \) B x A.

Let R be a relation on set N of natural numbers defined by R = {(x, y) : x, y\(\in\)N, x + 3y = 12} Find Range of R

Let R be a relation on the set Z of integers defined by R = {(x, y) : x, y \(\in\) Z, x² + y² = 25} Find R in roster form

Let A and B be two sets, such that A x B consists of 6 elements. If 3 elements of A x B are (1, 4), (2, 6) and (3, 6), then find A x B and B x A.

Determine the domain and range of the relation R, where R = {(2x+3, x³)} : x is a prime number less than 10}.