Advertisements
Advertisements
Question
Describe the following sets in set-builder form:
{2, 4, 6, 8 .....}
Advertisements
Solution
Set-builder form:
To describe a set, a variable x (each element of the set) is written inside braces. Then, after putting a colon, the common property P(x) possessed by each element of the set is written within braces.
\[ {x: x = 2n, n \in N}\]
APPEARS IN
RELATED QUESTIONS
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:
{2, 4, 8, 16, 32}
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
List all the elements of the following set:
F = {x : x is a consonant in the English alphabet which precedes k}.
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} |
Which of the following collection are sets? Justify your answer:
The collection of all girls in your class.
Which of the following collection is set? Justify your answer:
The collection of ten most talented writers of India.
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 all question in this chapter.
List all the elements of the following sets:
\[A = \left\{ x: x^2 \leq 10, x \in Z \right\}\]
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.
Write the set of all positive integers whose cube is odd.
Which of the following statement are correct?
Write a correct form of each of the incorrect statements.
\[a \subset \left\{ a, b, c \right\}\]
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ b, c \right\} \subset \left\{ a, \left\{ b, c \right\} \right\}\]
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?\[\left\{ \left\{ \phi \right\} \right\} \subset A\]
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 \[\left( A \cap C \right)'\]
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
10 _____ A
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ C).
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∩ B ∩ C)
Write the following interval in Set-Builder form
`(-∞, 5]`
Write the following interval in Set-Builder form.
(2, 5]
Write the following interval in Set-Builder form
[– 3, 4)
A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?
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}
Write the following sets in the roaster form.
C = {x : x2 + 7x – 8 = 0, x ∈ R}
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}
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 n + 1
Write the following sets in the roaster from:
C = {x | x is a positive factor of a prime number p}
Write the following sets in the roaster form:
E = `{w | (w - 2)/(w + 3) = 3, w ∈ R}`
Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to ______.
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 ______.
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
