English

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 ______.

Advertisements
Advertisements

Question

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 ______.

Options

  • reflexive

  • symmetric

  • transitive

  • none of these

MCQ
Fill in the Blanks
Advertisements

Solution

None of these.

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 (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
Chapter 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (6) | Page 104

RELATED QUESTIONS

Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.


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

(iii) R is a relation from {11, 12, 13} to (8, 10, 12] defined by y = x − 3.

 

Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N


Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N

(iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ∈ N × N

 

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


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


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


If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(x, y) : x, y ∈ A × B and x > y}


If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.


A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is


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

 

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


If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P


Let A = {6, 8} and B = {1, 3, 5}
Show that R1 = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R2 = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation


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

R2 = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`


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

R3 = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}


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

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


Select the correct answer from given alternative.

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


Select the correct answer from given alternative.

A relation between A and B 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

R1 = {(1, 4), (1, 5), (1, 6)}


Answer the following:

R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is symmentric


Answer the following:

Show that the following is an equivalence relation

R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}


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

R3 = {(2, –1), (7, 7), (1, 3)}


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

{(x, y) | y = x + 3, x, y are natural numbers < 10}


A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M), and an Executive Officer (E). The company provides ₹ 10,000, ₹ 25,000, ₹ 50,000, and ₹ 1,00,000 as salaries to the people who work in the categories A, C, M, and E respectively. If A1, A2, A3, A4, and A5 were Assistants; C1, C2, C3, C4 were Clerks; M1, M2, M3 were managers and E1, E2 was Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram


Multiple Choice Question :

If there are 1024 relation from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is


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 = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence


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 equivalence


Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai


Choose the correct alternative:

The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one of the following is true?


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

h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}


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

g = `"n", 1/"n" |"n"` is a positive integer


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 ______.


Which statement defines a relation from set \(A\) to set \(B\)?


Which statement about images in a function is correct?


If \(R\) is a relation from \(A\) to \(B\), what is its co-domain?


For a relation \(R\), the range is the set of all:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×