मराठी

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. - Mathematics

Advertisements
Advertisements

प्रश्न

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.

Advertisements

उत्तर

(i) A relation R from the set [2, 3, 4, 5, 6] to the set [1, 2, 3] is defined by x = 2y.
Putting y = 1, 2, 3 in x = 2y, we get:
x = 2, 4, 6
∴ R = {(2, 1), (4, 2), (6, 3)}

shaalaa.com
Fundamental Concepts of Ordered Pairs and Relations - Ordered Pairs
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Relations - Exercise 2.3 [पृष्ठ २०]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 2 Relations
Exercise 2.3 | Q 5.1 | पृष्ठ २०

संबंधित प्रश्‍न

If the ordered pairs (x, −1) and (5, y) belong to the set {(ab) : b = 2a − 3}, find the values of x and y


If a ∈ [−1, 2, 3, 4, 5] and b ∈ [0, 3, 6], write the set of all ordered pairs (ab) 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 (ab) such that a divides b and a < b.


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:
(xy) ∈ R ⇔ x is relatively prime to y
Express R as a set of ordered pairs and determine its domain and range.


Let A be the set of first five natural numbers and let R be a relation on A defined as follows:
(xy) ∈ R ⇔ x ≤ y
Express R and R−1 as sets of ordered pairs. Determine also (i) the domain of R−1 (ii) the range of R.


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 (xy) ∈ 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 (xy) ∈ R ⇔ x divides y.


Let R be a relation in N defined by (xy) ∈ 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) {(xy) : y = 3xx ∈ {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) {(xy) : 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:

{(xy) : x + y = 3, xy, ∈ [0, 1, 2, 3]}

 

 


Express the function f : X → given by f(x) = x+ 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}


If `(x/3+1, y-2/3)` = `(5/3,1/3),`find the values of x and y.


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}


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×