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 Mathematics and Science but not in English
Solution
Let the number of students 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 equation (iv) and (vii)
We get b + 4 = 6
∴ b = 2
From equation (v) and (vii)
We get 4 + f = 7
∴ f = 3
From equation (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
∴ Number of students who passed in Mathematics and Science but not in English, f = 3.
APPEARS IN
RELATED QUESTIONS
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 the set-builder form:
{2, 4, 8, 16, 32}
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
Describe the following sets in Roster form:
{x ∈ N : x2 < 25};
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ b, c \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
Which of the following statemen are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
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?
\[\phi \in A\]
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 = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\phi \in A\]
If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\]
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cap B \right)' = A' \cup B'\]
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Write the following interval in Set-Builder form
`(-∞, 5]`
Answer the following:
Write down the following set in set-builder form
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
Write the following sets in the roaster form.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
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 form:
D = {t | t3 = t, t ∈ R}
If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}.Write Y in the roaster form.
128 ∈ {y | the sum of all the positive factors of y is 2y}
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
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 more than one subject 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 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 French and Sanskrit but not English
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 ______.
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
