हिंदी

Write the relation in the Roster Form. State its domain and range R1 = {(a, a2)/a is prime number less than 15}

Advertisements
Advertisements

प्रश्न

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

R1 = {(a, a2)/a is prime number less than 15}

योग
Advertisements

उत्तर

R1 = {(a, a2)/a is prime number less than 15}

∴ a = 2, 3, 5, 7, 11, 13

∴ a2 = 4, 9, 25, 49, 121, 169

∴ R1 = {(2, 4), (3, 9), (5, 25), (7, 49), (11, 121), (13, 169)}

∴ Domain (R1)

= {a/a is a prime number less than 15}

= {2, 3, 5, 7, 11, 13}

Range (R1)

= {a2/a is a prime number less than 15}

= {4, 9, 25, 49, 121, 169}

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

संबंधित प्रश्न

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.


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?


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


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 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

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


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


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:

(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N

 

 


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

 

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 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


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

R4 = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}


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

R7 = {(a, b)/a, b ∈ N, a + b = 6}


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

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


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:

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?

R2 = {(–1, 1)}


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


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 :

The range of the relation R = {(x, x2) | x is a prime number less than 13} is ________


Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the 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 transitive


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 transitive


Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation


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


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 equivalence


Choose the correct alternative:

Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is


If R1 = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of R1.


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 ______.


Which condition must hold for a relation to be a function from \(A\) to \(B\)?


In the ordered pair \((a,b)\), what are \(a\) and \(b\), respectively?


The Cartesian product \(A\times A\) has \(9\) elements and contains \((-1,0)\) and \((0,1)\). What is \(A\)?


For \(A=\{-1,0,1\}\), which ordered pair is a remaining element of \(A\times A\) besides \((-1,0)\) and \((0,1)\)?


Let \(A=\{1,2,3,4,5\}\), \(B=\{1,4,5\}\), and \((x,y)\in R\) imply \(x

For \(R=\{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)\}\) from \(A\) to \(B=\{1,4,5\}\), which statement is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×