Advertisements
Advertisements
Question
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?
Advertisements
Solution
Let X ≡ set of all students
A ≡ set of students who drink apple juice
B ≡ set of students who drink orange juice
We are given the following:
n(X) = 425, n(A) = 115, n(B) = 160 and n(A ∩ B) = 80
The Venn diagram is shown below :
The number of students who drink neither apple juice nor orange juice
= n[(A ∪ B)']
= n(X) – n(A ∪ B)
= 425 – (35 + 80 + 80)
= 425 – 195
= 230
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
The collection of all natural numbers less than 100.
Identify whether the following is set or not? Justify your answer.
The collection of all even integers.
Identify whether the following is set or not? Justify your answer.
The collection of questions in this Chapter.
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:
D = {x : x is a prime number which is divisor of 60}
Which of the following collection are sets? Justify your answer:
The collection of all question in this chapter.
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 prime number which is a divisor of 60}
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Describe the following sets in set-builder form:
E = {0}
Describe the following sets in set-builder form:
{5, 25, 125 625}
List all the elements of the following set:
D = {x : x is a vowel in the word "EQUATION"}
List all the elements of the following set:
F = {x : x is a letter of the word "MISSISSIPPI"}
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
Which of the following statemen are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
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?
\[\phi \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\phi \in A\]
Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true?
Let \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible proper subsets each of the following set:
{1, 2},
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
4 _____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ A
Describe the following set in Set-Builder form
`{1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}`
In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take bot tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes at least one beverage, find the total number of students in the hostel.
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
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 B but not Chemical A
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}
Write the following sets in the roaster form:
D = {t | t3 = t, t ∈ R}
128 ∈ {y | the sum of all the positive factors of y is 2y}
State which of the following statement is true and which is false. Justify your answer.
3 ∉ {x | x4 – 5x3 + 2x2 – 112x + 6 = 0}
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.
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
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 ______.
If A and B are any two sets, then A – B is equal to ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
