मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

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 transitive

Advertisements
Advertisements

प्रश्न

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 transitive

बेरीज
Advertisements

उत्तर

∴ (1, 2), (2, 3) ∈ R but (1, 3) ∉ R

∴ R is not transitive

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Sets and Relations - Miscellaneous Exercise 5.2 [पृष्ठ १०५]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 5 Sets and Relations
Miscellaneous Exercise 5.2 | Q II. (9) (c) | पृष्ठ १०५

संबंधित प्रश्‍न

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?


The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`

The relation g is defined by  g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`

Show that f is a function and g is not a function.


Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.

 

Determine the domain and range of the relation R defined by

(ii) R = {(xx3) : x is a prime number less than 10}

 

Determine the domain and range of the relations:

(i) R = {(ab) : a ∈ N, a < 5, b = 4}


Determine the domain and range of the relations:

(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and}  \left| a \right| \leq 3 \right\}\]

 


Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(xy) : 3x − y = 0, where xy ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.


If n(A) = 3, n(B) = 4, then write n(A × A × B).

 

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


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


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


If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =


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


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

 

R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 is


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


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


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

R7 = {(a, b)/a, b ∈ N, a + b = 6}


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

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


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:

Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}


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


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


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


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 reflexive


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


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


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 transitive


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?


Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.


Is the following relation a function? Justify your answer

R2 = {(x, |x |) | x is a real number}


Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.


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 ______.


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 ______.


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


Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?

f is a function from A to B

Justify your answer in case.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×