हिंदी

Let the Relation R Be Defined on N by Arb Iff 2a + 3b = 30. Then Write R as a Set of Ordered Pairs

Advertisements
Advertisements

प्रश्न

Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs

Advertisements

उत्तर

As, R = {(ab) : 2a + 3b = 30; ab ∈ N}

So, R = {(3, 8), (6, 6), (9, 4), (12, 2)}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations - Exercise 1.3 [पृष्ठ ३०]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 1 Relations
Exercise 1.3 | Q 23 | पृष्ठ ३०

संबंधित प्रश्न

Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1.


Given an example of a relation. Which is symmetric but neither reflexive nor transitive.


Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.


Given a non-empty set X, consider P(X), which is the set of all subsets of X. Define the relation R in P(X) as follows:

For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.


Let A be the set of all human beings in a town at a particular time. Determine whether the following relation is reflexive, symmetric and transitive:

 R = {(x, y) : x and y work at the same place}


The following relation is defined on the set of real numbers.

aRb if 1 + ab > 0

Find whether relation is reflexive, symmetric or transitive.


Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.


If = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?


Defines a relation on :

x + y = 10, xy∈ N

Determine the above relation is reflexive, symmetric and transitive.


Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.


Let Z be the set of integers. Show that the relation
 R = {(a, b) : a, b ∈ Z and a + b is even}
is an equivalence relation on Z.


If R and S are relations on a set A, then prove that R and S are symmetric ⇒ R ∩ S and R ∪ S are symmetric ?


Let R = {(a, a3) : a is a prime number less than 5} be a relation. Find the range of R.


The relation 'R' in N × N such that
(a, b) R (c, d) ⇔ a + d = b + c is ______________ .


A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?


Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .


If R is a relation on the set A = {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3)}, then R is ____________ .


Mark the correct alternative in the following question:

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m  L. Then, R is ______________ .


Mark the correct alternative in the following question:

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b  T. Then, 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.


For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.


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


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
an injective mapping from A to B


Give an example of a map which is neither one-one nor onto


The following defines a relation on N:
x + 4y = 10 x, y ∈ N.
Determine which of the above relations are reflexive, symmetric and transitive.


Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is ______.


An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.


If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.


Let R be the relation “is congruent to” on the set of all triangles in a plane 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 ____________.

An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Let R: B → B be defined by R = {(x, y): x and y are students of same sex}, Then this relation R is ____________.

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • Let R = `{ ("L"_1, "L"_2) ∶ "L"_1 bot "L"_2  "where"  "L"_1, "L"_2 in "L" }` which of the following is true?

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Answer the following using the above information.

  • Let R = {(L1, L2 ): L1 is parallel to L2 and L1: y = x – 4} then which of the following can be taken as L2?

If A is a finite set consisting of n elements, then the number of reflexive relations on A is


The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is


Let R = {(x, y) : x, y ∈ N and x2 – 4xy + 3y2 = 0}, where N is the set of all natural numbers. Then the relation R is ______.


Which relation is reflexive on \(A=\{1,2\}\)?


A relation \(R\) is transitive if which condition is satisfied?


Which relation satisfies the transitive condition for the pairs \((1,2)\) and \((2,3)\)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×