मराठी

If R is a Relation from Set a = (11, 12, 13) to Set B = (8, 10, 12) Defined by Y = X − 3, Then Write R−1. - Mathematics

Advertisements
Advertisements

प्रश्न

If R is a relation from set A = (11, 12, 13) to set B = (8, 10, 12) defined by y = x − 3, then write R−1.

 

उत्तर

Given:
A = (11, 12, 13) and B = (8, 10, 12)
R is defined by (y = x − 3) from A to B.
We know:
8 = 11-3

10 = 13 -3 

∴ R = {(11, 8), (13, 10)}
Or,
R-1 = {(8, 11), (10, 13)}

 
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Relations - Exercise 2.4 [पृष्ठ २५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 2 Relations
Exercise 2.4 | Q 5 | पृष्ठ २५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.


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


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.


Determine the domain and range of the relation R defined by

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

 

Let A = (xyz) and B = (ab). Find the total number of relations from A into B.

 

Let A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by {(ab) : ab ∈ A, b is exactly divisible by a}

(i) Writer R in roster form
(ii) Find the domain of R
(ii) Find the range of R. 


The adjacent figure shows a relationship between the sets P and Q. Write this relation in (i) set builder form (ii) roster form. What is its domain and range?


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


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


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 = {(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?

 

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

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


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

R7 = {(a, b)/a, b ∈ N, a + b = 6}


Select the correct answer from given alternative.

A relation between A and B is


Select the correct answer from given alternative.

If (x, y) ∈ R × R, then xy = x2 is a relation which 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)}


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, 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


Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`


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 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 reflexive


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 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 equivalence


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?


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?


Choose the correct alternative:

The number of relations on a set containing 3 elements is


Choose the correct alternative:

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is


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


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

t = {(x, 3) | x is a real number


Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×