Advertisements
Advertisements
प्रश्न
For any two sets A and B,\[A \cap \left( A \cup B \right) =\]
पर्याय
(a) A
(b) B
(c) ϕ
(d) none of these.
उत्तर
(a) A
\[A \cap (A \cup B) = (A \cap A) \cup (A \cap B) = A \cup (A \cap B) = A\]
\[\]
APPEARS IN
संबंधित प्रश्न
{a, b} ⊄ {b, c, a}
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{3, 4} ⊂ A
Write the given intervals in set-builder form:
[6, 12]
Decide, among the following sets, which sets are subsets of one and another:
A = {x : x ∈ R and x satisfy x2 – 8x + 12 = 0},
B = {2, 4, 6}, C = {2, 4, 6, 8, …}, D = {6}.
Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A ⊂ B and B ∈ C, then A ∈ C
Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If A ⊄ B and B ⊄ C, then A ⊄ C
If a set contains n elements, then write the number of elements in its power set.
Write the number of elements in the power set of null set.
Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that \[A \cup B\]
If A and B are two sets such that \[A \subset B\], then write B' − A' in terms of A and B.
Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that \[A \cup B\] can have.
If \[A = \left\{ \left( x, y \right) : y = \frac{1}{x}, 0 \neq x \in R \right\}\]and\[B = \left\{ \left( x, y \right) : y = - x, x \in R \right\}\] then write\[A \cap B\]
If \[A = \left\{ \left( x, y \right) : y = e^x , x \in R \right\} and B = \left\{ \left( x, y \right) : y = e^{- x} , x \in R \right\}\]write\[A \cap B\]
If A and B are two sets such that \[n \left( A \right) = 115, n \left( B \right) = 326, n \left( A - B \right) = 47,\] then write \[n \left( A \cup B \right)\]
The number of subsets of a set containing n elements is
If A = {1, 3, 5, B} and B = {2, 4}, then
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{a, b, c} _____ {b, c, d}
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is a triangle in a plane} _____ {x : x is a rectangle in the plane}
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
1 ∈ A
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{1, 2, 5} ∈ A
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{1, 2, 3} ⊂ A
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
Φ ∈ A
Write the following interval in Set-Builder form:
(– 3, 0)
Given that N = {1, 2, 3, ..., 100}, then write the subset A of N, whose element are odd numbers.
Given that N = {1, 2, 3, ..., 100}, then write the subset B of N, whose element are represented by x + 2, where x ∈ N.
Given that N = {1, 2, 3, ... , 100}. Then write the subset of N whose element are perfect square numbers.
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n + 6
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by `n/2`
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n – 1
If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
a + 1 = 6, a ∈ Y
Suppose A1, A2, ..., A30 are thirty sets each having 5 elements and B1, B2, ..., Bn are n sets each with 3 elements, let \[\bigcup\limits_{i=1}^{30} A_{i} = \bigcup\limits_{j=1}^{n} B_{j}\] = and each element of S belongs to exactly 10 of the Ai’s and exactly 9 of the B,’S. then n is equal to ______.
If X = {8n – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.
State True or False for the following statement.
If A is any set, then A ⊂ A.
State True or False for the following statement.
Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.