List of top Mathematics Questions on Relations and Functions

Let $ A = \{2, 3, 4, 5, 6\} $. Let $ R $ be a relation on the set $ A \times A $ given by $ (x, y) R (z, w) $ if and only if $ x $ divides $ z $ and $ y \leq w $. Then the number of elements in $ R $ is _______.

Relation $R$ in the set $A = \{1,2,3,4,\ldots,16\}$ defined as $R = \{(x,y): 3x = y,\ x,y \in A\}$, then which of the following are correct ?
A. domain of $R = \{1, 2, 3, 4, 5\}$.
B. range of $R = \{3, 6, 9, 12, 15\}$.
C. $R$ is reflexive.
D. $R$ is not symmetric.
Choose the correct answer from the options given below:

A function $f: N \to N$, ($N$: set of natural numbers) defined by $f(x) = x^2 + x + 1$ is

A relation $R$ on set $A=\{1,2,3\}$ defined as $R=\{(1,2),(2,1),(2,2)\}$ is

The number of relations defined on the set $ \{a, b, c, d\} $ that are both reflexive and symmetric is equal to:

Let R be the relation in the set N given by $R = \{(a, b) : a = b - 2, b>6\}$. Which of the following is the correct answer?

$f(x) = (x + 1)^2$ for $x \ge 1$. $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is

If the domain of the function \[ f(x)=\frac{1}{\ln(10-x)}+\sin^{-1}\!\left(\frac{x+2}{2x+3}\right) \] is \[ (-\infty,-a]\ \cup\ (-1,b)\ \cup\ (b,c), \] then find the value of $ (b+c+3a) $.

Consider two sets \[ A = \{ x \in \mathbb{Z} : |(|x-3|-3)| \le 1 \} \] and \[ B = \left\{ x \in \mathbb{R} - \{1,2\} : \frac{(x-2)(x-4)}{x-1}\,\log_e(|x-2|) = 0 \right\}. \] Then the number of onto functions $ f : A \to B $ is equal to

Let $ A = \{0,1,2,\ldots,9\} $. Let $ R $ be a relation on $ A $ defined by $(x,y) \in R$ if and only if $ |x - y| $ is a multiple of $3$. Given below are two statements:
Statement I: $ n(R) = 36 $.
Statement II: $ R $ is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given below.

Show that the relation $ R $ in the set of natural numbers $ N \times N $ defined by $ (a, b)\, R\, (c, d) $ if $ a + d = b + c $ is an equivalence relation.