हिंदी

Write the relation in the Roster Form. State its domain and range R7 = {(a, b)/a, b ∈ N, a + b = 6} - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

R7 = {(a, b)/a, b ∈ N, a + b = 6}

योग
Advertisements

उत्तर

R7 = {(a, b)/a, b ∈ N, a + b = 6}

Here, a + b = 6

When a = 1, b = 5

When a = 2, b = 4

When a = 3, b = 3

When a = 4, b = 2

When a = 5, b = 1

∴ R7 = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}

Domain (R7) = {1, 2, 3, 4, 5}

Range (R7) = {5, 4, 3, 2, 1}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Sets and Relations - Exercise 5.2 [पृष्ठ १०३]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 5 Sets and Relations
Exercise 5.2 | Q 8. (vii) | पृष्ठ १०३

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?


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}}.


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:

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}


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.

 

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 R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Is the statement true?

(a, b) ∈ R implies (b, a) ∈ R

Justify your answer in case.


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, 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 from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is


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


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


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

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


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 ______.


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

R4 = {(4, 2), (2, 6), (5, 1), (2, 4)}


Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}


Answer the following:

Determine the domain and range of the following relation.

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


Answer the following:

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


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 reflexive


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


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

R1 = {(2, 1), (7, 1)}


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)}


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


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:

Let P denote the set of all straight lines in a plane. The relation R defined by “lRm if l is perpendicular to m”


Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the female members of a family. The relation R defined by “aRb if a is not a sister of b”


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


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 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 equivalence


Choose the correct alternative:

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


If R2 = {(x, y) | x and y are integers and x2 + y2 = 64} is a relation. Then find R2.


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 ______.


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 ______.


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×