Advertisements
Advertisements
Question
In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
Options
(a) 35
(b) 48
(c) 60
(d) 22
(e) 30
Solution
(c) 60
Let M, P and C denote the sets of students who have opted for mathematics, physics, and chemistry, respectively.
Here,
\[n\left( M \right)\] = 100,
\[n\left( P \right)\]=70 and \[n(C)\] = 40
Now,\[n\left( M \cap P \right) = 30, n\left( M \cap C \right) = 28, n\left( P \cap C \right) = 23 and n\left( M \cap P \cap C \right) = 18\]Number of students who opted for only mathematics:
\[n\left( M \cap P' \cap C' \right) = n\left\{ M \cap \left( P \cup C \right)' \right\}\]
\[ = n\left( M \right) - n\left\{ M \cap \left( P \cup C \right) \right\}\]
\[ = n\left( M \right) - n\left\{ \left( M \cap P \right) \cup \left( M \cap C \right) \right\}\]
\[ = n\left( M \right) - \left\{ n\left( M \cap P \right) + n\left( M \cap C \right) - n\left( M \cap P \cap C \right) \right\}\]
\[ = 100 - \left( 30 + 28 - 18 \right)\]
\[ = 60\]
Therefore, the number of students who opted for mathematics alone is 60
APPEARS IN
RELATED QUESTIONS
Identify whether the following set is finite or infinite.
{1, 2, 3, ...}
Identify whether the following set is finite or infinite.
{1, 2, 3, ... 99, 100}
Identify whether the following set is finite or infinite.
The set of positive integers greater than 100.
State whether the following set is finite or infinite:
The set of lines which are parallel to the x-axis.
State whether the following set is finite or infinite:
The set of letters in the English alphabet.
State whether the following set is finite or infinite:
The set of animals living on the earth.
State whether the following set is finite or infinite:
The set of circles passing through the origin (0, 0).
Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane
Which of the following sets are finite and which are infinite?
Set of letters of the English Alphabets
Which of the following sets are finite and which are infinite?
{x = ∈ N : x < 200}
Which of the following sets are finite and which are infinite?
{x ∈ Z : x < 5};
Which of the following sets are finite and which are infinite?
{x ∈ R : 0 < x < 1}.
Which of the following statements are true? Give reason to support your answer.
Every subset of an infinite set is infinite
Which of the following statements are true? Give reason to support your answer.
Every subset of a finite set is finite
Which of the following statements are true? Give reason to support your answer.
Every set has a proper subset
Which of the following statements are true? Give reason to support your answer.
{a, b, a, b, a, b, ...} is an infinite set
Which of the following statements are true? Give reason to support your answer.
{a, b, c} and {1, 2, 3} are equivalent sets
Which of the following statements are true? Give reason to support your answer.
A set can have infinitely many subsets.
State whether the following statements are true or false:
\[1 \in \left\{ 1, 2, 3 \right\}\]
State whether the following statements are true or false:
\[a \subset {b, c, a}\]
State whether the following statements are true or false:
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
State whether the following statements are true or false:
The set {x ; x + 8 = 8} is the null set.
Write which of the following statements are true? Justify your answer.
The set of all integers is contained in the set of all set of all rational numbers.
Write which of the following statement are true? Justify your answer.
The set of all crows is contained in the set of all birds.
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \subset A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true?\[\left\{ 2 \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible subsets of each of the following set:
\[\left\{ \phi \right\}\]
Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:
Suppose \[A_1 , A_2 , . . . , A_{30}\] are thirty sets each having 5 elements and \[B_1 , B_2 , . . . , B_n\] are n sets each with 3 elements. Let \[\cup^{30}_{i = 1} A_i = \cup^n_{j = 1} B_j = S\] and each element of S belong to exactly 10 of the \[A_i 's\]and exactly 9 of the\[B_j 's\] then n is equal to
Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are ______.
If A is a finite set containing n element, then number of subsets of A is ______.
