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 none of the three languages
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 none of the three language
= 50 – 30
= 20
APPEARS IN
संबंधित प्रश्न
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.
A team of eleven best-cricket batsmen of the world.
Identify whether the following is set or not? Justify your answer.
A collection of novels written by the writer Munshi Prem Chand.
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
Write the following set in roster form:
B = {x : x is a natural number less than 6}
Write the following set in the set-builder form:
{5, 25, 125, 625}
Write the following set in the set-builder form:
{2, 4, 6, …}
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
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:
12 ...... A
Describe the following sets in Roster form:
{x : x is a letter before e in the English alphabet}
Describe the following sets in Roster form:
{x ∈ N : x2 < 25};
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in set-builder form:
B={1,1/2 ,1/3, 1/4,1/5,...........};
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 statement are correct?
Write a correct form of each of the incorrect statements.
\[a \subset \left\{ a, b, c \right\}\]
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 = {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?
\[\phi \in A\]
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 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:
8 ____ A
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Describe the following set in Set-Builder form
{0}
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
Write the following interval in Set-Builder form.
(2, 5]
Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then, write the following sets containing all numbers represented by n2
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
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 class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither?
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
Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to ______.
Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.
