Advertisements
Advertisements
प्रश्न
State True or False for the following statement.
Let sets R and T be defined as
R = {x ∈ Z | x is divisible by 2}
T = {x ∈ Z | x is divisible by 6}. Then T ⊂ R
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
R and T can be represented in roster form as follows:
R = {…,-8, -6, -4, -2, 0, 2, 4, 6, 8,….}
T = {…,-18, -12, -6, 0, 6, 12, 18,….}
Since, every element of T is present in R.
So, T ⊂ R
APPEARS IN
संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of all natural numbers less than 100.
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}
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
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:
−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 ∈ N : x = 2n, n ∈ N};
Describe the following sets in Roster form:
{x : x is a prime number which is a divisor of 60}
Describe the following set in Roster form:
The set of all letters in the word 'Trigonometry'
Describe the following sets in set-builder form:
B={1,1/2 ,1/3, 1/4,1/5,...........};
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.
\[\left\{ b, c \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
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 = {{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? \[2 \subset A\]
Write down all possible subsets of each of the following set:
{a}
Write down all possible proper subsets each of the following set:
{1, 2, 3}
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:
8 ____ A
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
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.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
State which of the following statement is true and which is false. Justify your answer.
35 ∈ {x | x has exactly four positive factors}.
128 ∈ {y | the sum of all the positive factors of y is 2y}
State which of the following statements is true and which is false. Justify your answer.
496 ∉ {y | the sum of all the positive factors of y is 2y}.
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 English but not Sanskrit
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 at least one of the three languages
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
