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\[A \cap B\]
Advertisements
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
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{2, 3, 4} _____ {1, 2, 3, 4, 5}
{a, e} ⊂ {x : x is a vowel in the English alphabet}
{a, b} ⊄ {b, c, a}
{a} ⊂ {a. b, c}
Write the following as interval:
{x : x ∈ R, – 4 < x ≤ 6}
Write the given intervals in set-builder form:
(–3, 0)
Write the following interval in set-builder form:
[–23, 5)
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
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
If a set contains n elements, then write the number of elements in its power set.
If A and B are two sets such that \[A \subset B\], then write B' − A' in terms of A and 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 \[n \left( A \right) = 20, n \left( B \right) = 25\]\text{ and } \[n \left( A \cup B \right) = 40\], then write \[n \left( A \cap B \right)\]
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 \[n \left( A \cup B \right)\]
Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:
{x : x is a circle in the plane} _____ {x : x is a circle in the same plane with radius 1 unit}
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?
{3, 4} ∈ A
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?
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.
State true or false for the following statement given below:
Let R and S be the sets defined as follows:
R = {x ∈ Z | x is divisible by 2}
S = {y ∈ Z | y is divisible by 3}
then R ∩ S = φ
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 4n
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
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.
State True or False for the following statement.
Q ∪ Z = Q, where Q is the set of rational numbers and Z is the set of integers.
