English

Write the relation in the Roster Form. State its domain and range R2 = {(a,1a)/0<a≤5,a∈N}

Advertisements
Advertisements

Question

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

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

Sum
Advertisements

Solution

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

∴ R2 = `{(1, 1), (2, 1/2), (3, 1/3),(4, 1/4), (5, 1/5)}`

Domain of R2 = {a/0 < a ≤ 5, a ∈ N}

= {1, 2, 3, 4, 5}

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

= `{1, 1/2, 1/3, 1/4, 1/5}`

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Sets and Relations - Exercise 5.2 [Page 103]

APPEARS IN

RELATED QUESTIONS

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


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.


If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.


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.


For the relation R1 defined on R by the rule (ab) ∈ R1 ⇔ 1 + ab > 0. Prove that: (ab) ∈ R1 and (b , c) ∈ R1 ⇒ (ac) ∈ R1 is not true for all abc ∈ R.


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

(iii) (ab) R (cd) and (cd) R (ef) ⇒ (ab) R (ef) for all (ab), (cd), (ef) ∈ N × N

 

If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).


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

 

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


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


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)


Express {(x, y) / x2 + y2 = 100, where x, y ∈ W} as a set of ordered pairs


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}


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:

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


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

R2 = {(–1, 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)}


Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R


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


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”


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


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?


Choose the correct alternative:

Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which 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.

s = {(n, n2) | 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 ______.


Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×