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प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of all months of a year beginning with the letter J.
उत्तर
The collection of all months of a year beginning with J is (January, June, and July), which is well defined, and hence, it forms a set. Hence, this collection is a set.
संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of ten most talented writers of India.
Identify whether the following is set or not? Justify your answer.
A team of eleven best-cricket batsmen of the world.
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 questions in this Chapter.
Write the following set in the set-builder form:
{3, 6, 9, 12}
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}`
Which of the following collection are sets? Justify your answer:
A collection of novels written by Munshi Prem Chand.
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:
0 ...... 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 : x is a prime number which is a divisor of 60}
List all the elements of the following sets:
\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\]
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:
\[\left\{ 1, 2, 3 \right\} \subset A\]
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:
\[\phi \in A\]
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?
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 subsets of each of the following set:
{a, b, c},
Write down all possible proper subsets each of the following set:
{1, 2, 3}
What is the total number of proper subsets of a set consisting of n elements?
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 = {1, 2, 3, 4}, = {2, 4, 6, 8} and C = {3, 4, 5, 6}.
Find \[\left( A \cap C \right)'\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
8 ____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ A
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
Describe the following set in Set-Builder form
{0}
Write the following interval in Set-Builder form:
[6, 12]
Answer the following:
Write down the following set in set-builder form
{10, 20, 30, 40, 50}
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}
State which of the following statement are true and which are false. Justify your answer.
37 ∉ {x | x has exactly two positive factors}
Write the following sets in the roaster from:
B = {x | x2 = x, x ∈ R}
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 none of the three languages
