Advertisements
Advertisements
Question
Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
\[\left\{ 6, 7, 8 \right\} \in A\]
Advertisements
Solution
True
APPEARS IN
RELATED QUESTIONS
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 roster form:
B = {x : x is a natural number less than 6}
Write the following set in roster form:
D = {x : x is a prime number which is divisor of 60}
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:
{3, 6, 9, 12}
List all the elements of the following set:
F = {x : x is a consonant in the English alphabet which precedes k}.
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:
9 ...... A
Describe the following sets in Roster form:
{x ∈ N : x2 < 25};
Describe the following sets in Roster form:
{x : x is a prime number which is a divisor of 60}
Describe the following sets in set-builder form:
C = {0, 3, 6, 9, 12, ...}
List all the elements of the following set:
D = {x : x is a vowel in the word "EQUATION"}
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"} |
Write the set of all vowels in the English alphabet which precede q.
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 = {{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?
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible proper subsets each of the following set:
{1}.
What is the total number of proper subsets of a set consisting of n elements?
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:
8 ____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
0 ____ 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 Set-Builder form
`{1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}`
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read Only one of the newspapers
In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take bot tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes at least one beverage, find the total number of students in the hostel.
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 A but not Chemical B
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?
State which of the following statement are true and which are false. Justify your answer.
7,747 ∈ {t | t is a multiple of 37}
Write the following sets in the roaster form:
D = {t | t3 = t, t ∈ R}
If Y = {x | x is a positive factor of the number 2p – 1 (2p – 1), where 2p – 1 is a prime number}.Write Y in the roaster form.
128 ∈ {y | the sum of all the positive factors of y is 2y}
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 English and Mathematics but not in Science.
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 only
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 more than one subject 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 at least one of the three languages
The set {x ∈ R : 1 ≤ x < 2} can be written as ______.
