मराठी

The Relation R Defined on the Set a = {1, 2, 3, 4, 5} by R = {(A, B) : | A2 − B2 | < 16} is Given by (A) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} (B) {(2, 2), (3, 2), (4, 2), (2, 4)} (C) {(3, 3),

Advertisements
Advertisements

प्रश्न

The relation R defined on the set A = {1, 2, 3, 4, 5} by
R = {(a, b) : | a2 − b2 | < 16} is given by ______________ .

पर्याय

  • {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}

  • {(2, 2), (3, 2), (4, 2), (2, 4)}

  • {(3, 3), (4, 3), (5, 4), (3, 4)}

  • none of these

MCQ
Advertisements

उत्तर

none of these

R is given by {(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3), (4, 5), (5, 4), (1, 3), (3, 1), (1, 4), (4, 1) ,(2, 4), (4, 2)}, which is not mentioned in (a), (b) or (c).

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations - Exercise 1.4 [पृष्ठ ३१]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 1 Relations
Exercise 1.4 | Q 4 | पृष्ठ ३१

संबंधित प्रश्‍न

Let N denote the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.


Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}.


Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1.


Given an example of a relation. Which is reflexive and transitive but not symmetric.


Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.


Three relations R1, R2 and R3 are defined on a set A = {a, b, c} as follows:
R1 = {(a, a), (a, b), (a, c), (b, b), (b, c), (c, a), (c, b), (c, c)}
R2 = {(a, a)}
R3 = {(b, c)}
R4 = {(a, b), (b, c), (c, a)}.

Find whether or not each of the relations R1, R2, R3, R4 on A is (i) reflexive (ii) symmetric and (iii) transitive.


Let A = {a, b, c} and the relation R be defined on A as follows: R = {(a, a), (b, c), (a, b)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.


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


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


Let n be a fixed positive integer. Define a relation R on Z as follows:
(a, b) ∈ R ⇔ a − b is divisible by n.
Show that R is an equivalence relation on Z.


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.


Let A = {3, 5, 7}, B = {2, 6, 10} and R be a relation from A to B defined by R = {(x, y) : x and y are relatively prime}. Then, write R and R−1.


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 the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : | a2- b2 | < 8}. Write R as a set of ordered pairs.


Write the smallest equivalence relation on the set A = {1, 2, 3} ?


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


S is a relation over the set R of all real numbers and it is given by (a, b) ∈ S ⇔ ab ≥ 0. Then, S is _______________ .


Mark the correct alternative in the following question:

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


Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6} Find (A × B) ∩ (A × C).


Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b)/a∈ A, b∈ B, a – b is an even number}. Show that R is an empty relation from A to B.


Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive


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


If A = {1, 2, 3, 4 }, define relations on A which have properties of being: 
symmetric but neither reflexive nor transitive


Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.


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.


Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?


Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.


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 ____________.

The relation > (greater than) on the set of real numbers is


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 'R' in a set 'A' is called reflexive, if


Which of the following is/are example of symmetric


Let f(x)= ax2 + bx + c be such that f(1) = 3, f(–2) = λ and f(3) = 4. If f(0) + f(1) + f(–2) + f(3) = 14, then λ is equal to ______.


lf A = {x ∈ z+ : x < 10 and x is a multiple of 3 or 4}, where z+ is the set of positive integers, then the total number of symmetric relations on A is ______.


Which statement defines a Universal Relation?


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


What should be checked to determine whether a relation is symmetric?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×