Advertisements
Advertisements
Question
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\[A \cap B\]
Solution
We have:
\[A = \left\{ \left( x, y \right) : y = \frac{1}{x}, 0 \neq x \in R \right\}\]
\[\left( 1, 1 \right), \left( 2, \frac{1}{2} \right), \left( 3, \frac{1}{3} \right), \left( 4, \frac{1}{4} \right)\]And, \[B = \left\{ \left( x, y \right) : y = - x, x \in R \right\}\]
=\[\left\{ \left( 1, - 1 \right), \left( 2, - 2 \right), \left( 3, - 3 \right), \left( 4, - 4 \right), . . . \right\}\]
Thus, we get:
\[A \cap B\]=\[\varnothing\]
APPEARS IN
RELATED QUESTIONS
{a} ⊂ {a. b, c}
{a} ∈ (a, b, c)
Write down all the subsets of the following set:
{a}
How many elements has P(A), if A = Φ?
Write the following as interval:
{x : x ∈ R, – 4 < x ≤ 6}
Write the given intervals in set-builder form:
(–3, 0)
Write the given intervals in set-builder form:
[6, 12]
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 x ∈ A and A ⊄ B, then x ∈ B
Write the number of elements in the power set of null set.
Let A = {x : x ∈ N, x is a multiple of 3} and B = {x : x ∈ N and x is a multiple of 5}. Write \[A \cap B\]
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 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
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 even natural number} _____ {x : x is an integer}
Let A = {1, 2, {3, 4}, 5}. The following statement is correct or incorrect and why?
{3, 4} ∈ A
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:
{1, 2, 3}
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 of N whose elements are even numbers.
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
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 is less than 6 and 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 ______.
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.
