Advertisements
Advertisements
Question
Identify whether the following is set or not? Justify your answer.
The collection of all natural numbers less than 100.
Solution
The collection of all natural numbers less than 100 is {1, 2, 3, 4, ...., 99}, a well-defined collection because one can definitely identify a number that belongs to this collection.
Hence, this collection is a set.
APPEARS IN
RELATED QUESTIONS
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 even integers.
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:
F = {x : x is a consonant in the English alphabet which precedes k}.
Which of the following collection are sets? Justify your answer:
The collection of difficult topics in mathematics.
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 letter before e in the English alphabet}
Describe the following sets in Roster form:
{x ∈ N : x is a prime number, 10 < x < 20};
Describe the following sets in Roster form:
{x ∈ R : x > x}.
Describe the following set in Roster form:
The set of all letters in the word 'Trigonometry'
Describe the following sets in set-builder form:
A = {1, 2, 3, 4, 5, 6}
Describe the following sets in set-builder form:
C = {0, 3, 6, 9, 12, ...}
Describe the following sets in set-builder form:
E = {0}
List all the elements of the following sets:
\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\]
List all the elements of the following set:
\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]
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.
\[\phi \subset \left\{ a, b, c \right\}\]
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?
\[\left\{ c, d \right\} \in A\]
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:
\[1 \in A\]
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\left\{ 6, 7, 8 \right\} \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ 1 \right\} \in A\]
Write down all possible subsets of each of the following set:
{0, 1},
Write down all possible subsets of each of the following set:
{1, {1}},
What is the total number of proper subsets of a set consisting of n elements?
Prove that:
\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\]
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
Write the following interval in Set-Builder form
(2, 5]
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.
A = {x | x is a positive integer less than 10 and 2x – 1 is an odd number}
Write the following sets in the roaster from:
B = {x | x2 = x, x ∈ R}
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
Write the following sets in the roaster form:
E = `{w | (w - 2)/(w + 3) = 3, w ∈ R}`
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 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
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.