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प्रश्न
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
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उत्तर
This is not a set.
"Most talented" is a subjective adjective that can mean different things to different people. The most skilled writers may be viewed differently by various people.
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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.
The collection of all boys in your class.
Write the following set in roster form:
C = {x : x is a two-digit natural number such that the sum of its digits is 8}
Write the following set in roster form:
F = The set of all letters in the word BETTER
Write the following set in the set-builder form:
{5, 25, 125, 625}
Write the following set in the set-builder form:
{2, 4, 6, …}
List all the elements of the following set:
A = {x : x is an odd natural number}
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”}
List all the elements of the following set:
E = {x : x is a month of a year not having 31 days}
Which of the following collection are sets? Justify your answer:
The collection of prime integers.
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
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 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:
{2, 4, 6, 8 .....}
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 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 = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\phi \in A\]
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? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
What is the total number of proper subsets of a set consisting of n elements?
Prove that:
\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
4 _____ A
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
Describe the following set in Set-Builder form
{0}
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, did not fail in any examination.
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.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
Given that E = {2, 4, 6, 8, 10}. If n represents any member of E, then, write the following sets containing all numbers represented by n2
Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8
Write the following sets in the roaster from:
A = {x : x ∈ R, 2x + 11 = 15}
Write the following sets in the roaster form:
F = {x | x4 – 5x2 + 6 = 0, x ∈ R}
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 Sanskrit 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 none of the three languages
Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to ______.
