Advertisements
Advertisements
प्रश्न
If `(x/3+1, y-2/3)` = `(5/3,1/3),`find the values of x and y.
उत्तर
It is given that `(x/3+1, y-2/3)` = `(5/3,1/3)`.
Since the ordered pairs are equal, the corresponding elements will also be equal.
Therefore, `x/3 + 1 = 5/3` and `y - 2/3 = 1/3`.
`x/3+1 = 5/3` `y - 2/3 = 1/3`
`=> x/3 = 5/3 - 1` `y - 2/3 = 2/3`
`=>x/3 = 2/3` => y = 1
=> x = 2
=> x = 2 and y = 1
APPEARS IN
संबंधित प्रश्न
If a ∈ [−1, 2, 3, 4, 5] and b ∈ [0, 3, 6], write the set of all ordered pairs (a, b) such that a + b= 5.
If a ∈ [2, 4, 6, 9] and b ∈ [4, 6, 18, 27], then form the set of all ordered pairs (a, b) such that a divides b and a < b.
Let A and B be two sets such that n(A) = 3 and n(B) = 2.
If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y, z are distinct elements.
State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:
If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.
A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:
(x, y) ∈ R ⇔ x is relatively prime to y
Express R as a set of ordered pairs and determine its domain and range.
Write the relation as the sets of ordered pairs:
(i) A relation R from the set [2, 3, 4, 5, 6] to the set [1, 2, 3] defined by x = 2y.
Write the relation as the sets of ordered pairs:
(ii) A relation R on the set [1, 2, 3, 4, 5, 6, 7] defined by (x, y) ∈ R ⇔ x is relatively prime to y.
Write the relation as the sets of ordered pairs:
(iii) A relation R on the set [0, 1, 2, ....., 10] defined by 2x + 3y = 12.
Write the relation as the sets of ordered pairs:
(iv) A relation R from a set A = [5, 6, 7, 8] to the set B = [10, 12, 15, 16,18] defined by (x, y) ∈ R ⇔ x divides y.
Let R be a relation in N defined by (x, y) ∈ R ⇔ x + 2y =8. Express R and R−1 as sets of ordered pairs.
Let A = {1, 2, 3} and\[R = \left\{ \left( a, b \right) : \left| a^2 - b^2 \right| \leq 5, a, b \in A \right\}\].Then write R as set of ordered pairs.
Write the following relations as sets of ordered pairs and find which of them are functions:
(a) {(x, y) : y = 3x, x ∈ {1, 2, 3}, y ∈ [3,6, 9, 12]}
Write the following relations as sets of ordered pairs and find which of them are functions:
(b) {(x, y) : y > x + 1, x = 1, 2 and y = 2, 4, 6}
Write the following relations as sets of ordered pairs and find which of them are functions:
{(x, y) : x + y = 3, x, y, ∈ [0, 1, 2, 3]}
Express the function f : X → R given by f(x) = x3 + 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}
Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:
x + y = 5
Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:
x + y < 5
Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:
x + y > 8
Express the following functions as set of ordered pairs and determine their range.
f : X → R, f(x) = x3 + 1, where X = {–1, 0, 3, 9, 7}
State True or False for the following statement.
The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y ∈ Z}.
