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 ?...