List of top Mathematics Questions on Sets and Relations

Let $A = \{1, 4, 7\}$ and $B = \{2, 3, 8\}$. Then the number of elements in the relation $R = \{ ((a_1, b_1), (a_2, b_2)) \in (A \times B) \times (A \times B) : a_1+b_2 \text{ divides } a_2+b_1 \}$ is :}

Let $ R=\{(x,y)\in \mathbb{N}\times\mathbb{N}:\log_e(x+y)\le2\} $. Then the minimum number of elements required to be added in $R$ to make it a transitive relation is ________.

Let \[ S=\{x\in[-\pi,\pi]:\sin x(\sin x+\cos x)=a,\; a\in\mathbb{Z}\}. \] Then $n(S)$ is equal to:

The relation $R$ on the set of real numbers defined by \[ R=\{(a,b):a\leq b^2\} \] is:
• [(A)] Reflexive
• [(B)] Not symmetric
• [(C)] Neither reflexive nor transitive
• [(D)] Transitive Choose the correct answer from the options given below:

If \[ R=\{(x,y)\mid x,y\in \mathbb{R},\ x^2+y^2=1\} \] is a relation in $\mathbb{R}$, then $R$ is:

Consider the relation R on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab>0$. Then, among the statements:
I. The number of elements in R is 17
II. R is an equivalence relation

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{a, b, c\}$ then total number of functions from $A$ to $B$ which are not onto are

Let $ A = \{2,3,4,5,6\} $ be a set. Consider $ R $ be a relation on $ A \times A $ such that $ (x,y) \, R \, (a,b) $ implies $ x $ divides $ a $ and $ y \leq b $, then total number of elements in $ R $ is:

If $ A = \{1,2,3,4,5,6\} $ and $ B = \{1,2,3,\ldots,9\} $, then the number of strictly increasing functions $ f : A \to B $ such that $ f(i) \neq i $ for all $ i = 1,2,3,4,5,6 $ is:

Let $ A = \{-3, -2, -1, 0, 1, 2, 3\} $. A relation $ R $ is defined such that $ xRy $ if $ y = \max(x, 1) $. The number of elements required to make it reflexive is $ l $, the number of elements required to make it symmetric is $ m $, and the number of elements in the relation $ R $ is $ n $. Then the value of $ l + m + n $ is equal to:

If the set $R = {(a, b) : a + 5b = 42, a, b \in \mathbb{N}}$ has $m$ elements and $\sum_{n=1}^m (1 + i^n) = x + iy$, where $i = \sqrt{-1}$, then the value of $m + x + y$ is:

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

Let $A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}$,} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where $[x]$ denotes the greatest integer function. Then,

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

Let $ Z $ be the set of all integers,
$ A = \{(x, y) \in Z \times Z : (x - 2)^2 + y^2 \leq 4\} $,
$ B = \{(x, y) \in Z \times Z : x^2 + y^2 \leq 4\} $ and
$ C = \{(x, y) \in Z \times Z : (x - 2)^2 + (y - 2)^2 \leq 4\} $
If the total number of relations from $ A \cap B $ to $ A \cap C $ is $ 2^p $, then the value of $ p $ is :

If $A = \{x \in \mathbb{R} : |x-2|>1\}$, $B = \{x \in \mathbb{R} : \sqrt{x^2-3}>1\}$, $C = \{x \in \mathbb{R} : |x-4| \geq 2\}$ and $\mathbb{Z}$ is the set of all integers, then the number of subsets of the set $(A \cap B \cap C)^c \cap \mathbb{Z}$ is _________.

Let S = 1, 2, 3, 4, 5, 6, 9. Then the number of elements in the set T={A $\subseteq$ S: A $\neq \emptyset$ and the sum of all the elements of A is not a multiple of 3} is _________.