Sets, Relations and Functions · Mathematics · NDA

Let $A = \{x \in \mathbb{R} : -1 <x <1\}$. Which of the following is/are bijective functions from A to itself?1. $f(x) = x|x|$2. $g(x) = \cos(\p...

Let $R$ be a relation on the open interval $(-1, 1)$ and is given by $R = \{(x, y) : |x + y| ...

For any three non-empty sets $A, B, C$, what is $$(A \cup B - \{(A - B) \cup (B - A) \cup (A \cap B)\})$$ equal to?

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{6, 7\}$. What is the number of onto functions from $A$ to $B$?

A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?

The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct? 1.&nb...

Let A = {1, 2, 3, ..., 20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where x, y ∈ A. Which of the following statements...

Consider the following statements:  1. The relation f defined by $f(x)= \begin{cases}x^3, & 0 \leq x \leq 2 \\ 4 x, & 2 \leq x...

Consider the following statements  1. A = (A ∪ B) ∪ (A - B), 2. A ∪ (B - A) = (A ∪ B) 3.&nbs...

What is the binary number equivalent to decimal number 1011 ?

A mapping f : A → B defined as $f(x)=\frac{2 x+3}{3 x+5}, x \in A$ If f is to be onto, then what are A and B equal to ?...

Consider the following statements : 1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z. 2. If f...

Consider the following statements : 1. The set of all irrational numbers between $\sqrt{2}$ and $\sqrt{5}$ is an infinite set. 2. The set ...

Let A = {7, 8, 9, 10, 11, 12, 13; 14, 15, 16} and let f ∶ A → N be defined by f(x) = the highest prime factor of x. How many elements are there in th...

Let R be a relation from N to N defined by R = {(x, y): x, y ∈ N and x2 = y3}. Which of the following are not correct? 1. (x, x) ∈ R for all x ∈...

Consider the following : 1. A ∩ B = A ∩ C ⇒ B = C 2. A ∪ B = A ∪ C ⇒ B = C Which of the above is/are correct ?

How many received medals in exactly two of the three sports ?

How many received medals in at least two of three sports ?

How many received medals in exactly one of three sports ?

Let z = [y] and y = [x] − x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z ?

If A = {{1, 2, 3}}, then how many elements are there in the power set of A?

Consider all the subsets of the set A = {1, 2, 3, 4}. How many of them are supersets of the set {4}?

Consider the following statements in respect of two non-empty sets A and B : 1. x ∉ (A ∪ B) ⇒ x ∉ A or x ∉ B 2. x ∉ (A ∩&nb...

Consider the following statements in respect of two non-empty sets A and B : 1. A ∪ B = A ∩ B if A = B 2. A Δ B = ϕ  i...

Consider the following statements in respect of the relation R in the set IN of natural numbers defined by xRy if x2 - 5xy + 4y2 = 0 : 1. R is reflex...

Consider the following statements in respect of any relation R on a set A : 1. If R is reflexive, then R-1 is also reflexive 2. If R is symmetr...