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प्रश्न
Write down all possible proper subsets each of the following set:
{1, 2, 3}
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उत्तर
{1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}
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संबंधित प्रश्न
Write the following set in roster form:
B = {x : x is a natural number less than 6}
Write the following set in the set-builder form:
{5, 25, 125, 625}
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 question in this chapter.
Which of the following collection are sets? Justify your answer:
The collection of prime integers.
Describe the following sets in Roster form:
{x ∈ R : x > x}.
Describe the following set in Roster form:
The set of all letters in the word 'Trigonometry'
Describe the following sets in set-builder form:
{1, 4, 9, 16, ..., 100}
List all the elements of the following set:
F = {x : x is a letter of the word "MISSISSIPPI"}
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 positive integers whose cube is odd.
Which of the following statement are correct?
Write a correct form of each of the incorrect statement.
\[\left\{ a \right\} \in \left\{ a, b, c \right\}\]
Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
\[\left\{ a, b, e \right\} \in A\]
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:
\[\left\{ 6, 7, 8 \right\} \in A\]
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? \[\left\{ \left\{ 2 \right\}, \left\{ 1 \right\} \right\} \not\subset A\]
Write down all possible subsets of each of the following set:
{a, b, c},
What is the total number of proper subsets of a set consisting of n elements?
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank space:
2 _____ A
Describe the following set in Roster form
C = {x/x = 2n + 1, n ∈ N}
Describe the following set in Set-Builder form
{0}
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)
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}
State which of the following statement are true and which are false. Justify your answer.
37 ∉ {x | x has exactly two positive factors}
Write the following sets in the roaster form:
D = {t | t3 = t, t ∈ R}
128 ∈ {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 more than one subject 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 French and English but not Sanskrit
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 S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then ______.
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 ______.
Given A = {0, 1, 2}, B = {x ∈ R | 0 ≤ x ≤ 2}. Then A = B.
