(B) Let $A, B,$ and $C$ be the sets of people who like product $A$,product $B$,and product $C$ respectively.Given:$n(A) = 21, n(B) = 26, n(C) = 29$$n(

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(B) Let $A, B,$ and $C$ be the sets of people who like product $A$,product $B$,and product $C$ respectively.Given:$n(A) = 21, n(B) = 26, n(C) = 29$$n(A \cap B) = 14, n(C \cap A) = 12, n(B \cap C) = 14$$n(A \cap B \cap C) = 8$To find the number of people who like product $C$ only,we use the formula:$n(C \text{ only}) = n(C) - [n(A \cap C) + n(B \cap C) - n(A \cap B \cap C)]$$n(C \text{ only}) = 29 - [12 + 14 - 8]$$n(C \text{ only}) = 29 - [26 - 8]$$n(C \text{ only}) = 29 - 18 = 11$Thus,$11$ people liked product $C$ only.

Class 11 Mathematics Set Theory Word Problem - Set Theory

Easy

In a survey,it was found that $21$ people liked product $A$,$26$ liked product $B$,and $29$ liked product $C$. If $14$ people liked products $A$ and $B$,$12$ people liked products $C$ and $A$,$14$ people liked products $B$ and $C$,and $8$ liked all three products,find how many people liked product $C$ only.

A
$9$
B
$11$
C
$13$
D
$15$

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In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

Easy

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There are exactly twelve Sundays in the period from January $1$ to March $31$ in a certain year. Then,the day corresponding to February $15$ in that year is

KVPY 2017

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$a, b, c, d, e, f, g, h$ are distinct elements in the set $\{-7, -5, -3, -2, 2, 4, 6, 13\}$. The minimum value of $(a+b+c+d)^2+(e+f+g+h)^2$ is

DifficultAP EAMCET 2022

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Let $S = \{1, 2, 3, \ldots, 40\}$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by $5$. What is the maximum number of elements possible in $A$?

MediumKVPY 2012

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An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to

EasyAP EAMCET 2020

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In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

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