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 English but not Sanskrit
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 English but not Sanskrit, b = 6
APPEARS IN
संबंधित प्रश्न
Write the following set in roster form:
D = {x : x is a prime number which is divisor of 60}
Write the following set in the set-builder form:
{2, 4, 8, 16, 32}
List all the elements of the following set:
F = {x : x is a consonant in the English alphabet which precedes k}.
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
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
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in set-builder form:
C = {0, 3, 6, 9, 12, ...}
Describe the following sets in set-builder form:
D = {10, 11, 12, 13, 14, 15};
List all the elements of the following set:
F = {x : x is a letter of the word "MISSISSIPPI"}
Match each of the sets on the left in the roster form with the same set on the right described in the set-builder form:
| (i) | {A, P, L, E} | (i) | x : x + 5 = 5, x ∈ Z |
| (ii) | {5, −5} | (ii) | {x : x is a prime natural number and a divisor of 10} |
| (iii) | {0} | (iii) | {x : x is a letter of the word "RAJASTHAN"} |
| (iv) | {1, 2, 5, 10,} | (iv) | {x: x is a natural number and divisor of 10} |
| (v) | {A, H, J, R, S, T, N} | (v) | x : x2 − 25 = 0 |
| (vi) | {2, 5} | (vi) | {x : x is a letter of the word "APPLE"} |
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
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?
\[\left\{ a, b, c \right\} \subset A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\phi \in A\]
Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?
Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true?
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:
{0, 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}.
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
8 ____ A
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
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ A
Write the following interval in Set-Builder form
`(6, ∞)`
Write the following sets in the roaster form.
A = {x | x is a positive integer less than 10 and 2x – 1 is an odd number}
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 only
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 Sanskrit only
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 at least one of the three languages
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
If A and B are any two sets, then A – B is equal to ______.
