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प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of all natural numbers less than 100.
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उत्तर
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.
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संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of questions in this Chapter.
Write the following set in roster form:
E = The set of all letters in the word TRIGONOMETRY
Write the following set in the set-builder form:
{2, 4, 8, 16, 32}
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:
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 all question in this chapter.
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:
12 ...... 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:
0 ...... A
Describe the following sets in Roster form:
The set of all letters in the word 'Better'.
Write the set of all vowels in the English alphabet which precede q.
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 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:
\[\left\{ \left\{ 4, 5 \right\} \right\} \subset A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? \[\left\{ 1 \right\} \in A\]
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}.
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:
4 _____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ 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}
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ 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
Answer the following:
Write down the following set in set-builder form
{a, e, i, o, u)
Write the following sets in the roaster form.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
State which of the following statement are true and which are false. Justify your answer.
37 ∉ {x | x has exactly two positive factors}
State which of the following statement are true and which are false. Justify your answer.
7,747 ∈ {t | t is a multiple of 37}
In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither?
Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then ______.
In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of persons who read neither is ______.
