Let A = {a, b, c} and B = {1, 2, 3, 4}. Then | vedclass

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

Question

(B) The set $C$ consists of all functions $f: A \rightarrow B$ such that $2 \in f(A)$ and $f$ is not one-one.Total functions from $A$ to $B$ where $2

Vedclass · Accepted Answer

$19$

Vedclass · Answer

(B) The set $C$ consists of all functions $f: A ightarrow B$ such that $2 \in f(A)$ and $f$ is not one-one.Total functions from $A$ to $B$ where $2 \in f(A)$ is calculated as: (Total functions) - (Functions where $2 
otin f(A)$).Total functions $= 4^3 = 64$.Functions where $2 
otin f(A)$ (i.e.,$f: A ightarrow \{1, 3, 4\}$) $= 3^3 = 27$.So,functions where $2 \in f(A) = 64 - 27 = 37$.Now,we subtract the one-one functions where $2 \in f(A)$ from this total.Number of one-one functions from $A$ to $B$ is $P(4, 3) = 4 	imes 3 	imes 2 = 24$.In these $24$ one-one functions,how many contain $2$ in their range? If $2$ is not in the range,the function maps $A$ to ${1, 3, 4}$. Number of one-one functions $= P(3, 3) = 3 	imes 2 	imes 1 = 6$.So,one-one functions where $2 \in f(A) = 24 - 6 = 18$.Therefore,the number of functions that are not one-one and $2 \in f(A) = 37 - 18 = 19$.

Let $A = \{a, b, c\}$ and $B = \{1, 2, 3, 4\}$. Then the number of elements in the set $C = \{f : A \rightarrow B \mid 2 \in f(A) \text{ and } f \text{ is not one-one}\}$ is

Similar Questions

Given two finite sets $A$ and $B$ such that $n(A) = 2$ and $n(B) = 3$. Then,the total number of relations from $A$ to $B$ is:

If $x$ is real,then the value of the expression $\frac{x^2 + 14x + 9}{x^2 + 2x + 3}$ lies between

Write down the power set of $C = \{1, \{2\}\}$.

The solution set of $8x \equiv 6 \pmod{14}$,$x \in \mathbb{Z}$,is

If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$,then $(A \cap B) \cup (A \cap C)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module