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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.
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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
Write the following set in roster form:
D = {x : x is a prime number which is divisor of 60}
Write the following set in the set-builder form:
{2, 4, 6, …}
Which of the following collection are sets? Justify your answer:
The collection of difficult topics in mathematics.
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.
Describe the following sets in Roster form:
{x ∈ R : x > x}.
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'.
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"} |
Which of the following statement are correct?
Write a correct form of each of the incorrect statements.
\[a \subset \left\{ a, b, c \right\}\]
Which of the following statemen are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a, b \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
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 = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
\[\left\{ a, b, e \right\} \in A\]
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 \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
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}.
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:
2 _____ A
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
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
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
Select the correct answer from given alternative.
In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus are
Answer the following:
Write down the following set in set-builder form
{10, 20, 30, 40, 50}
Answer the following:
Write down the following set in set-builder form
{a, e, i, o, u)
Answer the following:
In a school there are 20 teachers who teach Mathematics or Physics. Of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?
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 form:
D = {t | t3 = t, t ∈ R}
Determine whether the following statement is true or false. Justify your answer.
For all sets A, B, and C, A – (B – C) = (A – B) – C
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
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
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is ______.
If sets A and B are defined as A = `{(x, y) | y = 1/x, 0 ≠ x ∈ "R"}` B = {(x, y) | y = – x, x ∈ R}, then ______.
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
