Advertisements
Advertisements
प्रश्न
Describe the following set in Set-Builder form
{0, –1, 2, –3, 4, –5, 6, ...}
Advertisements
उत्तर
Let D = {0, –1, 2, –3, –5, 6, ...}
The even integers are 0, 2, 4, 6, ... and have positive sign
The odd integers are 1, 3, 5, ... and have negative sign
∴ D can be written in set builder form as:
D = {x/x = (–1)n–1 × (n – 1), n ∈ N}
APPEARS IN
संबंधित प्रश्न
Identify whether the following is set or not? Justify your answer.
The collection of ten most talented writers of India.
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 the set-builder form:
{2, 4, 6, …}
List all the elements of the following set:
A = {x : x is an odd natural number}
List all the elements of the following set:
C = {x : x is an integer, x2 ≤ 4}
List all the elements of the following set:
D = {x : x is a letter in the word “LOYAL”}
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 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 prime integers.
Describe the following sets in Roster form:
{x ∈ N : x is a prime number, 10 < x < 20};
Describe the following sets in set-builder form:
C = {0, 3, 6, 9, 12, ...}
Describe the following sets in set-builder form:
{1, 4, 9, 16, ..., 100}
List all the elements of the following set:
\[B = \left\{ x: x = \frac{1}{2n - 1}, 1 \leq n \leq 5 \right\}\]
Which of the following statement 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 = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[\left\{ c, d \right\} \in A\]
Let A = {a, b, {c, d}, e}. Which of the following statement are false and why?
\[a \in A\]
Let \[A = \left\{ \phi, \left\{ \phi \right\}, 1, \left\{ 1, \phi \right\}, 2 \right\}\]Which of the following are true? \[\left\{ 1 \right\} \in A\]
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 \[\left( A \cap B \right)' = A' \cup B'\]
Describe the following set in Roster form
A = {x/x is a letter of the word 'MOVEMENT'}
Describe the following set in Set-Builder form
{0, ±1, ±2, ±3}
If A = {x/6x2 + x – 15 = 0}, B = {x/2x2 – 5x – 3 = 0}, C = {x/2x2 – x – 3 = 0} then find (A ∪ B ∪ C).
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
`(-∞, 5]`
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?
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 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 statement is true and which is false. Justify your answer.
35 ∈ {x | x has exactly four positive factors}.
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 Mathematics only
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 ______.
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 ______.
A survey shows that 63% of the people watch a News Channel whereas 76% watch another channel. If x% of the people watch both channel, 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 ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
