Let $f$ be the subset of $\mathbb{Z} \times \mathbb{Z}$ defined by $f = \{(ab, a + b) : a, b \in \mathbb{Z}\}$. Is $f$ a function from $\mathbb{Z}$ to $\mathbb{Z}$? Justify your answer.

Let $A = \{1, 2, 3,...,14\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : 3x – y = 0, \text{where } x, y \in A\}$. Write down its domain, codomain and range.

A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (ii) $f(7)$

The function f{x}=logx/x is increasing in the interval ?

Let $f = \{(1,1), (2,3), (0,–1), (–1, –3)\}$ be a function from $\mathbb{Z}$ to $\mathbb{Z}$ defined by $f(x) = ax + b$, for some integers $a, b$. Determine $a, b$.

If $A \times B = \{(a, x),(a, y), (b, x), (b, y)\}$. Find $A$ and $B$.

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? (ii) $f$ is a function from $A$ to $B$. Justify your answer in each case.

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 $A \times A$.

Let $A = \{1, 2\}$, $B = \{1, 2, 3, 4\}$, $C = \{5, 6\}$ and $D = \{5, 6, 7, 8\}$. Verify that (i) $A \times (B \cap C) = (A \times B) \cap (A \times C)$.

Let $R$ be a relation from $\mathbb{N}$ to $\mathbb{N}$ defined by $R = \{(a, b) : a, b \in \mathbb{N} \text{ and } a = b^2\}$. Are the following true? (i) $(a,a) \in R$, for all $a \in \mathbb{N}$. Justify your answer in each case.

Find the number of points of discontinuity:
 where [] denotes the greatest integer function.

Find the domain of the function $f(x) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}$.

A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (iii) $f(–3)$

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 function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (i) $t(0)$

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) $t(–10)$

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (i) Write $R$ in roster form.

The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (iv) The value of $C$, when $t(C) = 212$.

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) $t(28)$

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