Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let us use Venn diagram method.
Total number of students = 50
⇒ n(U) = 50
Number of students who study French = 17
⇒ n(F) = 17
Number of students who study English = 13
⇒ n(E) = 13
Number of students who study Sanskrit = 15
⇒ n(S) = 15
Number of students who study French and English = 9
⇒ n(F ∩ E) = 9
Number of students who study English and Sanskrit = 4
⇒ n(E ∩ S) = 4
Number of students who study French and Sanskrit = 5
⇒ n(F ∩ S) = 5
Number of students who study French, English and Sanskrit = 3
⇒ n(F ∩ E ∩ S) = 3
n(F) = 17
a + b + d + e = 17 ......(i)
n(E) = 13
b + c + e + f = 13 ......(ii)
n(S) = 15
d + e + f + g = 15 ......(iii)
n(F ∩ E) = 9
∴ b + e = 9 ......(iv)
n(E ∩ S) = 4
∴ e + f = 4 .......(v)
n(F ∩ S) = 5
∴ d + e = 5 ......(vi)
n(E ∩ F ∩ S) = 3
∴ e = 3 .......(vii)
From (iv)
b + 3 = 9
⇒ b = 9 – 3 = 6
From (v)
3 + f = 4
⇒ f = 4 – 3 = 1
From (vi)
d + 3 = 5
⇒ d = 5 – 3 = 2
Now from equation (i)
a + 6 + 2 + 3 = 17
⇒ a = 17 – 11
⇒ a = 6
Now from equation (ii)
6 + c + 3 + 1 = 13
⇒ c = 13 – 10
⇒ c = 3
From equation (iii)
2 + 3 + 1 + g = 15
⇒ g = 15 – 6
⇒ g = 9
Number of students who study French and Sanskrit but not English, d = 2
APPEARS IN
संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of all months of a year beginning with the letter J.
Identify whether the following is set or not? Justify your answer.
The collection of ten most talented writers of India.
Identify whether the following is set or not? Justify your answer.
The collection of all boys in your class.
Write the following set in the set-builder form:
{2, 4, 8, 16, 32}
Write the following set in the set-builder form:
{1, 4, 9, ....., 100}
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
| (i) | {1, 2, 3, 6} | (a) | {x : x is a prime number and a divisor of 6} |
| (ii) | {2, 3} | (b) | {x : x is an odd natural number less than 10} |
| (iii) | {M, A, T, H, E, I, C, S} | (c) | {x : x is natural number and divisor of 6} |
| (iv) | {1, 3, 5, 7, 9} | (d) | {x : x is a letter of the word MATHEMATICS} |
Which of the following collection are sets? Justify your answer:
The collection of all question in this chapter.
Which of the following collection are sets? Justify your answer:
The collection of prime integers.
If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:
−4 ...... A
If A = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], then insert the appropriate symbol ∈ or ∉ in each of the following blank space:
0 ...... A
Describe the following sets in Roster form:
{x ∈ R : x > x}.
Describe the following sets in set-builder form:
E = {0}
Describe the following sets in set-builder form:
{1, 4, 9, 16, ..., 100}
List all the elements of the following set:
\[C = \left\{ x: x \text{ is an integer }, - \frac{1}{2} < x < \frac{9}{2} \right\}\]
List all the elements of the following set:
D = {x : x is a vowel in the word "EQUATION"}
Which of the following statements are correct?
Write a correct form of each of the incorrect statement.
\[a \in {\left\{ a \right\}, b}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ \left\{ c, d \right\} \right\} \subset A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \in A\]
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:
\[\left\{ \left\{ 4, 5 \right\} \right\} \subset A\]
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 proper subsets each of the following set:
{1, 2},
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cap B \right)' = A' \cup B'\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
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 Only one of the newspapers
In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take bot tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes at least one beverage, find the total number of students in the hostel.
There are 260 persons with skin disorders. If 150 had been exposed to chemical A, 74 to chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A but not Chemical B
Write the following interval in Set-Builder form
`(-∞, 5]`
Write the following sets in the roaster form.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
State which of the following statement are true and which are false. Justify your answer.
37 ∉ {x | x has exactly two positive factors}
State which of the following statement are true and which are false. Justify your answer.
7,747 ∈ {t | t is a multiple of 37}
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8
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
Write the following sets in the roaster from:
A = {x : x ∈ R, 2x + 11 = 15}
Write the following sets in the roaster from:
B = {x | x2 = x, x ∈ R}
State which of the following statement is true and which is false. Justify your answer.
35 ∈ {x | x has exactly four positive factors}.
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 none of the three languages
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 ______.
