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Describe the following set in Roster form C = {x/x = 2n + 1, n ∈ N} - Mathematics and Statistics

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प्रश्न

Describe the following set in Roster form

C = {x/x = 2n + 1, n ∈ N}

बेरीज
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उत्तर

C = {x/x = 2n + 1, n ∈ N}

= {3, 5, 7, 9, ...}

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Sets and Relations - Exercise 5.1 [पृष्ठ ९७]

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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 1. (iii) | पृष्ठ ९७

संबंधित प्रश्‍न

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

5 _____ A


Write the following set in roster form:

A = {x : x is an integer and –3 ≤ x < 7}


List all the elements of the following set:

A = {x : x is an odd natural number}


List all the elements of the following set:

B = `{x : x  "is an integer", -1/2 < x < 9/2}`


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 difficult topics in mathematics.

 


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: 

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 : x is a prime number which is a divisor of 60} 


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) {APLE} (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) {xx is a natural number and divisor of 10}
(v) {AHJRSTN} (v) x : x2 − 25 = 0
(vi) {2, 5} (vi) {x : x is a letter of the word "APPLE"}

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 statemen 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: 

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


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 subsets of each of the following set:

{1, {1}}, 


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

{1, 2},


If A is any set, prove that: \[A \subseteq \phi \Leftrightarrow A = \phi .\] 


Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cap B \right)' = A' \cup B'\] 


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, did not fail in any examination.


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


Write the following interval in Set-Builder form:

[6, 12]


Write the following interval in Set-Builder form

[– 3, 4)


Answer the following:

Write down the following set in set-builder form

{10, 20, 30, 40, 50}


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?


Write the following sets in the roaster form.
A = {x | x is a positive integer less than 10 and 2x – 1 is an odd number}


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

28 ∈ {y | the sum of the all positive factors of y is 2y}


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

7,747 ∈ {t | t is a multiple of 37}


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 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.


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 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?


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 ______.


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 ______.


The set {x ∈ R : 1 ≤ x < 2} can be written as ______.


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