" in the set of N (Natural number) is | Shaalaa.com" />" in the set of N (Natural number) is " />" in the set of N (Natural number) is, Basics of Relations & Functions" />
English

Select the correct answer from given alternative. The relation ">" in the set of N (Natural number) is

Advertisements
Advertisements

Question

Select the correct answer from given alternative.

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

Options

  • Symmetric

  • Reflexive

  • Transitive

  • Equivalence relation

MCQ
Advertisements

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Sets and Relations - Miscellaneous Exercise 5.1 [Page 104]

APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
Chapter 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (7) | Page 104

RELATED QUESTIONS

Let A = {1, 2, 3, …, 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.


Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.


Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.


Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.


Find the inverse relation R−1 in each of the cases:

(ii) R = {(xy), : xy ∈ N, x + 2y = 8}


Let A = (3, 5) and B = (7, 11). Let R = {(ab) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.


Determine the domain and range of the relation R defined by

(i) R = [(xx + 5): x ∈ (0, 1, 2, 3, 4, 5)]


Let R = [(xy) : xy ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.


Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(xy) : x − yis odd}. Write R in roster form. 


If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is


If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation on Z, then the domain of R is ______.


Let R be a relation from a set A to a set B, then


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


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


Write the relation in the Roster Form. State its domain and range

R5 = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}


Write the relation in the Roster Form. State its domain and range

R6 = {(a, b)/a ∈ N, a < 6 and b = 4}


Write the relation in the Roster Form. State its domain and range

R8 = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}


Select the correct answer from given alternative.

Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.


Select the correct answer from given alternative

If A = {a, b, c} The total no. of distinct relations in A × A is


Answer the following:

If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range

R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}


Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}


Answer the following:

Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.


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

R4 = {(7, –1), (0, 3), (3, 3), (0, 7)}


A Relation R is given by the set `{(x, y)/y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}`. Determine its domain and range


Multiple Choice Question :

Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to B is ________.


Let A = {9, 10, 11, 12, 13, 14, 15, 16, 17} and let f : A → N be defined by f(n) = the highest prime factor of n ∈ A. Write f as a set of ordered pairs and find the range of f


Discuss the following relation for reflexivity, symmetricity and transitivity:

The relation R defined on the set of all positive integers by “mRn if m divides n”


Discuss the following relation for reflexivity, symmetricity and transitivity:

On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”


On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is transitive


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


Choose the correct alternative:

The number of relations on a set containing 3 elements is


Is the given relation a function? Give reasons for your answer.

t = {(x, 3) | x is a real number


Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.


Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×