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Write the following interval in Set-Builder form (– 3, 4) - Mathematics and Statistics

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प्रश्न

Write the following interval in Set-Builder form

[– 3, 4)

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उत्तर

[– 3, 4) = {x/x ∈ R, – 3 ≤ x < 4}

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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. (vi) | पृष्ठ ९८

संबंधित प्रश्‍न

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

A collection of novels written by the writer Munshi Prem Chand.


Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

5 _____ A


Write the following set in the set-builder form:

{3, 6, 9, 12}


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}


Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}
(ii) {2, 3} (b) {x : x is an odd natural number less than 10}
(iii) {M, A, T, H, E, I, C, S} (c) {x : x is natural number and divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}

List all the elements of the following set: 

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


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.  

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


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

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


Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false: 

\[\left\{ 1, 2, 3 \right\} \subset A\] 

 


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? \[2 \subset A\]


Let \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\] 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 proper subsets each of the following set:

{1, 2},


Prove that: 

\[A \subseteq B, B \subseteq C \text{ and } C \subseteq A \Rightarrow A = C .\] 


Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:

8 ____ A


Describe the following set in Roster form

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


Describe the following set in Set-Builder form

{0, –1, 2, –3, 4, –5, 6, ...}


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


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 at least one of the newspapers


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 neither Marathi and English newspaper


Write the following interval in Set-Builder form

`(6, ∞)`


Answer the following:

Write down the following set in set-builder form

{10, 20, 30, 40, 50}


Answer the following:

Write down the following set in set-builder form

{a, e, i, o, u)


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?


Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n + 5 = 8


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}


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 at least one of the three languages


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 ______.


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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