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Write the following interval in Set-Builder form: [6, 12] - Mathematics and Statistics

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प्रश्न

Write the following interval in Set-Builder form:

[6, 12]

बेरीज
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उत्तर

The interval [6, 12] can be written in set-builder form as {x : x ∈ R, 6 ≤ x ≤ 12}.

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पाठ 5: Sets and Relations - Exercise 5.1 [पृष्ठ ९८]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 5 Sets and Relations
Exercise 5.1 | Q 12. (ii) | पृष्ठ ९८

संबंधित प्रश्‍न

Identify whether the following is set or not? Justify your answer.

The collection of all months of a year beginning with the letter J.


Identify whether the following is set or not? Justify your answer.

A team of eleven best-cricket batsmen of the world.


Identify whether the following is set or not? Justify your answer.

The collection of all natural numbers less than 100.


Identify whether the following is set or not? Justify your answer.

The collection of all even integers.


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:

B = {x : x is a natural number less than 6}


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:

E = The set of all letters in the word TRIGONOMETRY


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:

{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:

A = {x : x is an odd natural number}


Which of the following collection are sets? Justify your answer: 

The collection of all question in this chapter.


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: 

−4 ...... A 


Describe the following sets in Roster form: 

{x ∈ N : x2 < 25}; 


Describe the following sets in set-builder form:

B={1,1/2 ,1/3, 1/4,1/5,...........};


Describe the following sets in set-builder form: 

 D = {10, 11, 12, 13, 14, 15}; 


Describe the following sets in set-builder form: 

{2, 4, 6, 8 .....}


List all the elements of the following set: 

\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]


List all the elements of the following set: 

D = {x : x is a vowel in the word "EQUATION"}


Write the set of all vowels in the English alphabet which precede q.


Write the set of all positive integers whose cube is odd.


Write the set \[\left\{ \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50} \right\}\]  in the set-builder form.


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.

\[\left\{ a \right\} \subset \left\{ \left\{ a \right\}, b \right\}\] 


Let A = {ab, {cd}, e}. Which of the following statement are false and why? 

\[\left\{ c, d \right\} \in A\] 


Let A = {ab, {cd}, e}. Which of the following statement are false and why? 

\[\left\{ \left\{ c, d \right\} \right\} \subset A\]


Let A = {ab, {cd}, e}. Which of the following statement are false and why? 

\[a \in A\]


Let A = {ab, {cd}, e}. Which of the following statement are false and why?

\[\left\{ a, b, c \right\} \subset A\]


Let A = {ab, {cd}, e}. Which of the following statement are false and why? 

\[\phi \in A\]


Let A = {ab, {cd}, 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: 

\[\left\{ \left\{ 4, 5 \right\} \right\} \subset A\] 


Let\[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true? 

\[\left\{ \phi \right\} \in A\]

 


Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] 


Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\] Which of the following are true?\[\left\{ \left\{ \phi \right\} \right\} \subset A\]

 


Write down all possible subsets of each of the following set: 

 {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: 

{abc}, 


Write down all possible proper subsets each of the following set:

{1, 2},


Write down all possible proper subsets each of the following set: 

{1}. 


Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, = {2, 4, 6, 8} and C = {3, 4, 5, 6}.

Find \[\left( A \cap C \right)'\]


Describe the following set in Roster form

B = `{x//x  "is an integer", -3/2 < x < 9/2}`


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


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


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


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


There are 260 persons with skin disorders. If 150 had been exposed to the chemical A, 74 to the chemical B, and 36 to both chemicals A and B, find the number of persons exposed to Chemical A or Chemical B


Write the following interval in Set-Builder form.

(2, 5]


Answer the following:

Write down the following set in set-builder form

{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}


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?


State which of the following statement are true and which are false. Justify your answer.

37 ∉ {x | x has exactly two positive factors}


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 


Write the following sets in the roaster from:
A = {x : x ∈ R, 2x + 11 = 15}


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}


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.


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}.


Determine whether the following statement is true or false. Justify your answer.

For all sets A, B, and C, A – (B – C) = (A – B) – C


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


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 English and Sanskrit but not French


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 class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Then, the number of students who play neither is ______.


If sets A and B are defined as A = `{(x, y) | y = 1/x, 0 ≠ x ∈ "R"}` B = {(x, y) | y = – x, x ∈ R}, then ______.


Let S = {x | x is a positive multiple of 3 less than 100}
P = {x | x is a prime number less than 20}. Then n(S) + n(P) is ______.


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


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