Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the number of students who passed in Mathematics M, E be in English and S be in Science.
Then n(U) = 100
n(M) = 12
n(E) = 15
n(S) = 8
n(E ∩ M) = 6
n(M ∩ S) = 7
n(E ∩ S) = 4
And n(E ∩ M ∩ S) = 4
Let us draw a Venn diagram.
According to the Venn diagram, we get
a + b + d + e = 15 ......(i)
b + c + e + f = 12 ......(ii)
d + e + f + g = 8 .....(iii)
n(E ∩ M) = 6
∴ b + e = 6 ......(iv)
n(M ∩ S) = 7
∴ e + f = 7 ......(v)
n(E ∩ S) = 4
∴ d + e = 4 ......(vi)
And n(E ∩ M ∩ S) = 4
∴ e = 4 ......(vii)
From equations (iv) and (vii)
We get b + 4 = 6
∴ b = 2
From equations (v) and (vii)
We get 4 + f = 7
∴ f = 3
From equations (vi) and (vii)
We get d + 4 = 4
∴ d = 0
From equation (i) we get
a + b + d + e = 15
⇒ a + 2 + 0 + 4 = 15
⇒ a = 9
From equation (ii)
b + c + e + f = 12
⇒ 2 + c + 4 + 3 = 12
⇒ c = 3
From equation (iii)
d + e + f + g = 8
⇒ 0 + 4 + 3 + g = 8
⇒ g = 1
∴ The number of students who passed in English and Mathematics but not in Science, b = 2.
APPEARS IN
RELATED QUESTIONS
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.
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
5 _____ A
Write the following set in roster form:
B = {x : x is a natural number less than 6}
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}
List all the elements of the following set:
E = {x : x is a month of a year not having 31 days}
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} |
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:
12 ...... 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:
−2 ...... A
Describe the following sets in Roster form:
{x ∈ N : x is a prime number, 10 < x < 20};
Describe the following sets in set-builder form:
D = {10, 11, 12, 13, 14, 15};
List all the elements of the following set:
\[C = \left\{ x: x \text{ is an integer }, - \frac{1}{2} < x < \frac{9}{2} \right\}\]
Write the set of all positive integers whose cube is odd.
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.
\[\left\{ b, c \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \subset A\]
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 = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\left\{ 6, 7, 8 \right\} \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[2 \subset A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true?\[\left\{ \left\{ \phi \right\} \right\} \subset A\]
Write down all possible proper subsets each of the following set:
{1, 2},
What is the total number of proper subsets of a set consisting of n elements?
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
`{1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}`
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
Write the following interval in Set-Builder form.
(2, 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?
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}
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 form:
F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
128 ∈ {y | the sum of all the positive factors of y is 2y}
Determine whether the following statement is true or false. Justify your answer.
For all sets A, B, and C, A – (B – C) = (A – B) – C
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 Mathematics 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 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 ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
