English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative: Let R be the universal relation on a set X with more than one element. Then R is

Advertisements
Advertisements

Question

Choose the correct alternative:

Let R be the universal relation on a set X with more than one element. Then R is

Options

  • not reflexive

  • not symmetric

  • transitive

  • none of the above

MCQ
Advertisements

Solution

transitive

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Sets, Relations and Functions - Exercise 1.5 [Page 47]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 1 Sets, Relations and Functions
Exercise 1.5 | Q 13 | Page 47

RELATED QUESTIONS

The given figure shows a relationship between the sets P and Q. Write this relation

  1. in set-builder form.
  2. in roster form.

What is its domain and range?


Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b ∈ A, b is exactly divisible by a}.

  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.

Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.


If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.


Determine the domain and range of the relations:

(i) R = {(ab) : a ∈ N, a < 5, b = 4}


Let A = {ab}. List all relations on A and find their number.

 

If R is a relation defined on the set Z of integers by the rule (xy) ∈ R ⇔ x2 + y2 = 9, then write domain of R.


If R = {(xy) : xy ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.


If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R is


If R is a relation on a finite set having n elements, then the number of relations on A is


Identify which of if the following relations are reflexive, symmetric, and transitive.

Relation Reflexive Symmetric Transitive
R = {(a, b) : a, b ∈ Z, a – b is an integer}      
R = {(a, b) : a, b ∈ N, a + b is even} x
R = {(a, b) : a, b ∈ N, a divides b}      
R = {(a, b) : a, b ∈ N, a2 – 4ab + 3b2 = 0}      
R = {(a, b) : a is sister of b and a, b ∈ G = Set of girls}      
R = {(a, b) : Line a is perpendicular to line b in a plane}      
R = {(a, b) : a, b ∈ R, a < b}      
R = {(a, b) : a, b ∈ R, a ≤ b3}      

Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) is


Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}


Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R2 = {(–1, 1)}


Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}


On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is reflexive


Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?


If R = {(x, y): x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is ______.


A relation on the set A = {x : |x| < 3, x ∈ Z}, where Z is the set of integers is defined by R = {(x, y) : y = |x| ≠ –1}. Then the number of elements in the power set of R is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×