Advertisements
Advertisements
Question
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
Advertisements
Solution
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 only, a = 6
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
The collection of all boys in your class.
Identify whether the following is set or not? Justify your answer.
The collection of questions in this Chapter.
Write the following set in roster form:
C = {x : x is a two-digit natural number such that the sum of its digits is 8}
Write the following set in roster form:
F = The set of all letters in the word BETTER
Write the following set in the set-builder form:
{2, 4, 8, 16, 32}
List all the elements of the following set:
B = `{x : x "is an integer", -1/2 < x < 9/2}`
Which of the following collection are sets? Justify your answer:
The collection of all girls in your class.
Which of the following collection are sets? Justify your answer:
The collection of difficult topics in mathematics.
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:
{x : x is a letter before e in the English alphabet}
List all the elements of the following set:
F = {x : x is a letter of the word "MISSISSIPPI"}
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \in A\]
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?
\[\left\{ a, b, c \right\} \subset A\]
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:
{0, 1},
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
Describe the following set in Set-Builder form
{0}
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ C).
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:
[6, 12]
A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?
Answer the following:
Write down the following set in set-builder form
{10, 20, 30, 40, 50}
Answer the following:
Write down the following set in set-builder form
{a, e, i, o, u)
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
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
Write the following sets in the roaster form:
E = `{w | (w - 2)/(w + 3) = 3, w ∈ R}`
Write the following sets in the roaster form:
F = {x | x4 – 5x2 + 6 = 0, 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}.
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed in English and Mathematics but not in Science.
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 ______.
If sets A and B are defined as A = `{(x, y) | y = 1/x, 0 ≠ x ∈ "R"}` B = {(x, y) | y = – x, x ∈ R}, then ______.
Let S = {x | x is a positive multiple of 3 less than 100}
P = {x | x is a prime number less than 20}. Then n(S) + n(P) is ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
