मराठी

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______. - Mathematics

Advertisements
Advertisements

प्रश्न

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______.

पर्याय

  • Reflexive

  • Symmetric

  • Transitive

  • None of these

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is symmetric.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations And Functions - Solved Examples [पृष्ठ ८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 1 Relations And Functions
Solved Examples | Q 18 | पृष्ठ ८

संबंधित प्रश्‍न

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

Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}.


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

Relation R in the set Z of all integers defined as R = {(x, y) : x − y is an integer}.


Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric.


The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4


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 is father of and y}


Test whether the following relation R1 is  (i) reflexive (ii) symmetric and (iii) transitive :

R1 on Q0 defined by (a, b) ∈ R1 ⇔ = 1/b.


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


Prove that the relation R on Z defined by
(a, b) ∈ R ⇔ a − b is divisible by 5
is an equivalence relation on Z.


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.


Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(ab) : | a2b| < 8}. Write as a set of ordered pairs.


Let R be the relation over the set of all straight lines in a plane such that  l1 R l2 ⇔ l 1⊥ l2. Then, R is _____________ .


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


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


If A = {1, 2, 3}, then a relation R = {(2, 3)} on A is _____________ .


The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} 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 relation S defined on the set R of all real number by the rule aSb if a  b is _______________ .


Mark the correct alternative in the following question:

Consider a 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 _____________ .


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.


Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.


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


R = {(a, b) / b = a + 1, a ∈ Z, 0 < a < 5}. Find the Range of R.


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


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


Let n be a fixed positive integer. Define a relation R in Z as follows: ∀ a, b ∈ Z, aRb if and only if a – b is divisible by n. Show that R is an equivalance relation


The following defines a relation on N:
x is greater than y, 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 ______.


Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.


Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.


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 ∀ a, b ∈ T. Then R is ____________.


Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.


Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.


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


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


A market research group conducted a survey of 2000 consumers and reported that 1720 consumers like product P1 and 1450 consumers like product P2. What is the least number that must have liked both the products?


If f(x + 2a) = f(x – 2a), then f(x) is:


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 ______.


Let R1 and R2 be two relations defined as follows :

R1 = {(a, b) ∈ R2 : a2 + b2 ∈ Q} and

R2 = {(a, b) ∈ R2 : a2 + b2 ∉ Q}, where Q is the set of all rational numbers. Then ______


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 ______.


Let N be the set of all natural numbers and R be a relation on N × N defined by (a, b) R (c, d) `⇔` ad = bc for all (a, b), (c, d) ∈ N × N. Show that R is an equivalence relation on N × N. Also, find the equivalence class of (2, 6), i.e., [(2, 6)].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×