Let S = {1, 2, 3, ldots, n} and A = {(a, b) m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The set $A = S 	imes S$ contains $n^2$ elements.$A$ subset $B$ of $A$ is a good subset if it contains all elements of the form $(x, x)$ for $x \i

Vedclass · Accepted Answer

$2^{n(n-1)}$

Vedclass · Answer

(C) The set $A = S 	imes S$ contains $n^2$ elements.$A$ subset $B$ of $A$ is a good subset if it contains all elements of the form $(x, x)$ for $x \in S$.There are $n$ such elements: $(1, 1), (2, 2), \ldots, (n, n)$.For $B$ to be a good subset,these $n$ elements must be present in $B$.The remaining elements in $A$ are those $(a, b)$ where $a 
eq b$. The number of such elements is $n^2 - n = n(n - 1)$.Each of these $n(n - 1)$ elements can either be in $B$ or not in $B$.Therefore,the number of ways to choose the remaining elements is $2^{n(n - 1)}$.Thus,the total number of good subsets is $2^{n(n - 1)}$.

Let $S = \{1, 2, 3, \ldots, n\}$ and $A = \{(a, b) \mid 1 \leq a, b \leq n\} = S \times S$. $A$ subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then,the number of good subsets of $A$ is

Similar Questions

Let $A$ and $B$ be two sets. Then

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements is incorrect and why? $\{ \{ 3, 4\} \} \subset A$

If $Q = \{x : x = \frac{1}{y}, y \in N\}$,then which of the following is true?

State which of the following sets are finite or infinite:
$A = \{ x : x \in \mathbb{N} \text{ and } x \text{ is prime} \}$

Determine the subset for the set $\{n(n+1)(2n+1) : n \in \mathbb{Z}\}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module