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प्रश्न
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read at least one of the newspapers
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उत्तर
Let M = set of individuals who read Marathi newspapers
E = set of individuals who read English newspapers
X = set of all literate individuals
∴ n(X) = 2000, n(M)
= `70/100xx2000`
= 1400
n(E) = `50/100xx2000` = 1000
n(M ∩ E) = `32.5/100xx2000` = 650
n(M ∪ E) = n(M) + n(E) − n(M ∩ E)
= 1400 + 1000 − 650
= 1750
No. of individuals who read at least one of the newspapers = n(M ∪ E) = 1750.
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संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of questions in this Chapter.
Write the following set in the set-builder form:
{2, 4, 8, 16, 32}
Describe the following sets in Roster form:
{x : x is a letter before e in the English alphabet}
Describe the following set in Roster form:
The set of all letters in the word 'Trigonometry'
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in set-builder form:
A = {1, 2, 3, 4, 5, 6}
Describe the following sets in set-builder form:
D = {10, 11, 12, 13, 14, 15};
Describe the following sets in set-builder form:
{1, 4, 9, 16, ..., 100}
List all the elements of the following set:
\[C = \left\{ x: x \text{ is an integer }, - \frac{1}{2} < x < \frac{9}{2} \right\}\]
Which of the following statements are correct?
Write a correct form of each of the incorrect statement.
\[a \in {\left\{ a \right\}, b}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a \right\} \subset \left\{ \left\{ a \right\}, b \right\}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\phi \subset \left\{ a, b, c \right\}\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[1 \in A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\left\{ 1, 2, 3 \right\} \subset A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]
Write down all possible subsets of each of the following set:
{a}
Write down all possible subsets of each of the following set:
{1, {1}},
Write down all possible proper subsets each of the following set:
{1, 2},
Write down all possible proper subsets each of the following set:
{1, 2, 3}
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
Describe the following set in Set-Builder form
{0, ±1, ±2, ±3}
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read neither Marathi and English newspaper
Write the following interval in Set-Builder form:
[6, 12]
Write the following interval in Set-Builder form
`(-∞, 5]`
Answer the following:
In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?
State which of the following statement are true and which are false. Justify your answer.
28 ∈ {y | the sum of the all positive factors of y is 2y}
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n is greater than 4
State which of the following statement is true and which is false. Justify your answer.
35 ∈ {x | x has exactly four positive factors}.
State which of the following statements is true and which is false. Justify your answer.
496 ∉ {y | the sum of all the positive factors of y is 2y}.
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study English and Sanskrit but not French
In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows:
French = 17, English = 13, Sanskrit = 15 French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study French and Sanskrit but not English
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is ______.
If A and B are any two sets, then A – B is equal to ______.
