Advertisements
Advertisements
प्रश्न
Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that \[A \cup B\]
Advertisements
उत्तर
\[\text{ We know that } n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ n\left( A \cup B \right) \text{ is minimum when } n\left( A \cap B \right) \text{ is maximum }\]
\[so, n\left( A \cap B \right) = 3\]
\[\text{ Hence }, n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right) \]
\[ = 3 + 6 - 3\]
\[ = 6\]
APPEARS IN
संबंधित प्रश्न
{a} ⊂ {a. b, c}
{a} ∈ (a, b, c)
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{3, 4} ⊂ A
How many elements has P(A), if A = Φ?
Write the following as interval:
{x : x ∈ R, – 4 < x ≤ 6}
Write the following as intervals: {x: x ∈ R, –12 < x < –10}
Write the following as intervals: {x : x ∈ R, 0 ≤ x < 7}
Write the following as intervals: {x : x ∈ R, 3 ≤ x ≤ 4}
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
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 x ∉ B, then x ∉ A
Write the number of elements in the power set of null set.
If A = {x ∈ C : x2 = 1} and B = {x ∈ C : x4 = 1}, then write A − B and B − A.
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\[A \cap B\]
The number of subsets of a set containing n elements is
For any two sets A and B,\[A \cap \left( A \cup B \right) =\]
If A = |1, 2, 3, 4, 5|, then the number of proper subsets of A is
In set-builder method the null set is represented by
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is a student of Class XI of your school} ____ {x : x student of your school}
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}
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is an equilateral triangle in a plane} _____ {x : x is a triangle in the same 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?
{Φ} ⊂ A
Write down all the subsets of the following set:
{a, b}
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.
State true or false for the following statement given below:
Q ∩ R = Q, where Q is the set of rational numbers and R is the set of real numbers.
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by n – 1
If X = {8n – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.
State True or False for the following statement.
The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.
