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

The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (ii) $t(28)$

Let $A$ and $B$ be two sets such that $n(A) = 3$ and $n(B) = 2$. If $(x, 1), (y, 2), (z, 1)$ are in $A \times B$, find $A$ and $B$, where $x$, $y$ and $z$ are distinct elements.

The Fig2.7 shows a relationship between the sets $P$ and $Q$. Write this relation (ii) roster form. What is its domain and range?

Let $A = \{1, 2\}$ and $B = \{3, 4\}$. Write $A \times B$. How many subsets will $A \times B$ have? List them.

The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (iii) $t(–10)$

Find the range of each of the following functions. (iii) $f(x) = x$, $x$ is a real number.

Let $R$ be the relation on $\mathbb{Z}$ defined by $R = \{(a,b): a, b \in \mathbb{Z}, a – b \text{ is an integer}\}$. Find the domain and range of $R$.

Find the range of each of the following functions. (ii) $f(x) = x^2 + 2$, $x$ is a real number.

$A = \{1, 2, 3, 5\}$ and $B = \{4, 6, 9\}$. Define a relation $R$ from $A$ to $B$ by $R = \{(x, y): \text{the difference between } x \text{ and } y \text{ is odd}; x \in A, y \in B\}$. Write $R$ in roster form.

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) \{(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)\}

The Fig2.7 shows a relationship between the sets $P$ and $Q$. Write this relation (i) in set-builder form. What is its domain and range?

Let $f = \{\left(x, \frac{x^2}{1+x^2}\right) : x \in \mathbb{R}\}$ be a function from $\mathbb{R}$ into $\mathbb{R}$. Determine the range of $f$.

The Cartesian product $A \times A$ has 9 elements among which are found $(–1, 0)$ and $(0,1)$. Find the set $A$ and the remaining elements of $A \times A$.

Determine the domain and range of the relation $R$ defined by $R = \{(x, x + 5) : x \in \{0, 1, 2, 3, 4, 5\}\}$.

Find the range of each of the following functions. (i) $f(x) = 2 – 3x, x \in \mathbb{R}, x > 0$.

Let $A =\{1,2,3,4\}$, $B = \{1,5,9,11,15,16\}$ and $f = \{(1,5), (2,9), (3,1), (4,5), (2,11)\}$. Are the following true? (i) $f$ is a relation from $A$ to $B$. Justify your answer in each case.

If $(\frac{x}{3} + 1, y - \frac{2}{3}) = (\frac{5}{3}, \frac{1}{3})$, find the values of $x$ and $y$.

Define a relation $R$ on the set $\mathbb{N}$ of natural numbers by $R = \{(x, y) : y = x + 5, x \text{ is a natural number less than } 4; x, y \in \mathbb{N}\}$. Depict this relationship using roster form. Write down the domain and the range.

A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (i) $f(0)$