Advertisements
Advertisements
Question
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} |
Solution
| (i) | {1, 2, 3, 6} | (c) | {x : x is natural number and divisor of 6} |
| (ii) | {2, 3} | (a) | {x : x is a prime number and a divisor of 6} |
| (iii) | {M, A, T, H, E, I, C, S} | (d) | {x : x is a letter of the word MATHEMATICS} |
| (iv) | {1, 3, 5, 7, 9} | (b) | {x : x is an odd natural number less than 10} |
APPEARS IN
RELATED QUESTIONS
Identify whether the following is set or not? Justify your answer.
The collection of all boys in your class.
Write the following set in the set-builder form:
{1, 4, 9, ....., 100}
List all the elements of the following set:
A = {x : x is an odd natural number}
List all the elements of the following set:
B = `{x : x "is an integer", -1/2 < x < 9/2}`
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
List all the elements of the following set:
D = {x : x is a letter in the word “LOYAL”}
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
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:
0 ...... A
Describe the following sets in Roster form:
{x : x is a letter before e in the English alphabet}
Describe the following sets in Roster form:
{x ∈ R : x > x}.
Describe the following sets in set-builder form:
E = {0}
List all the elements of the following set:
F = {x : x is a letter of the word "MISSISSIPPI"}
Match each of the sets on the left in the roster form with the same set on the right described in the set-builder form:
| (i) | {A, P, L, E} | (i) | x : x + 5 = 5, x ∈ Z |
| (ii) | {5, −5} | (ii) | {x : x is a prime natural number and a divisor of 10} |
| (iii) | {0} | (iii) | {x : x is a letter of the word "RAJASTHAN"} |
| (iv) | {1, 2, 5, 10,} | (iv) | {x: x is a natural number and divisor of 10} |
| (v) | {A, H, J, R, S, T, N} | (v) | x : x2 − 25 = 0 |
| (vi) | {2, 5} | (vi) | {x : x is a letter of the word "APPLE"} |
Write the set \[\left\{ \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50} \right\}\] in the set-builder form.
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 statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
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:
\[\phi \in A\]
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}.
If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
8 ____ A
In a class of 200 students who appeared in certain examinations, 35 students failed in CET, 40 in NEET and 40 in JEE, 20 failed in CET and NEET, 17 in NEET and JEE, 15 in CET and JEE, and 5 failed in all three examinations. Find how many students, failed in NEET or JEE entrance
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 the chemical A, 74 to the chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A or Chemical B
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:
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.
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 is greater than 4
Write the following sets in the roaster from:
B = {x | x2 = x, x ∈ R}
Write the following sets in the roaster form:
E = `{w | (w - 2)/(w + 3) = 3, w ∈ 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.
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.
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 English but not Sanskrit
