मराठी

If a = {2, 3, 4}, B = {1, 3, 7} and R = {(X, Y) : X ∈ A, Y ∈ B and X < Y} is a Relation from a to B, Then Write R−1.

Advertisements
Advertisements

प्रश्न

If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R−1.

बेरीज
Advertisements

उत्तर

Since R = {(x, y) : x ∈ A, y ∈ A and x < y},
R = {(2, 3), (2, 7), (3, 7), (4, 7)}
So, R-1 = {(3, 2), (7, 2), (7, 3), (7, 4)}

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations - Exercise 1.3 [पृष्ठ ३०]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 1 Relations
Exercise 1.3 | Q 8 | पृष्ठ ३०

संबंधित प्रश्‍न

Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive.


Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.


Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is the same as the distance of the point Q from the origin} is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with the origin as its centre.


Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is an equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, and 10. Which triangles among T1, T2 and T3 are related?


Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is ______.


Test whether the following relation R3 is (i) reflexive (ii) symmetric and (iii) transitive:

R3 on R is defined by (a, b) ∈ R3 `⇔` a2 – 4ab + 3b2 = 0.


If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?


Show that the relation '≥' on the set R of all real numbers is reflexive and transitive but not symmetric ?


Show that the relation R defined by R = {(a, b) : a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.


Let R be a relation on the set A of ordered pair of integers defined by (x, y) R (u, v) if xv = yu. Show that R is an equivalence relation.


Show that the relation R, defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have the same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right-angled triangle T with sides 3, 4 and 5?


Let O be the origin. We define a relation between two points P and Q in a plane if OP = OQ. Show that the relation, so defined is an equivalence relation.


If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.


Define an equivalence relation ?


Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.


Let R be a relation on the set N given by
R = {(a, b) : a = b − 2, b > 6}. Then,


R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .


Let R be a relation on N defined by x + 2y = 8. The domain of R is _______________ .


 If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is _____________ .


In the set Z of all integers, which of the following relation R is not an equivalence relation ?


Mark the correct alternative in the following question:

The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .


Mark the correct alternative in the following question:

For real numbers x and y, define xRy if `x-y+sqrt2` is an irrational number. Then the relation R is ___________ .


Show that the relation R on the set Z of all integers, given by R = {(a,b) : 2 divides (a-b)} is an equivalence relation.


If A = {a, b, c}, B = (x , y} find A × B.


Write the relation in the Roster form and hence find its domain and range :
R1 = {(a, a2) / a is prime number less than 15}


Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is ______.


Give an example of a map which is not one-one but onto


Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.


If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.


Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is ____________.


Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Let R ∶ B → B be defined by R = {(x, y): y is divisible by x} is ____________.

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Let R: B → B be defined by R = {(1,1),(1,2), (2,2), (3,3), (4,4), (5,5), (6,6)}, then R is ____________.

The relation R = {(1,1),(2,2),(3,3)} on {1,2,3} is ____________.


Find: `int (x + 1)/((x^2 + 1)x) dx`


In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea?


A relation in a set 'A' is known as empty relation:-


Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is ______.


Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?


For \(A=\{1,2\}\), which relation is the Identity Relation?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×