English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

Given A= {x, y, z) and B = {1, 2)

n(A) = 3 and n(B) = 2

Since n(A × B) = n(A) × n(B)

n(A x B) = 3 x 2 = 6.

The Number of relations from A to B is equal to the number of subsets of A x B.

Since A × B contains 6 elements.

=> Number of subsets of A × B = 26 = 64.

So, there are 64 relations from A to B.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations and Functions - Exercise 2.2 [Page 36]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 2 Relations and Functions
Exercise 2.2 | Q 8 | Page 36

RELATED QUESTIONS

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.


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


Let A = (3, 5) and B = (7, 11). Let R = {(ab) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.


Let A = {ab}. List all relations on A and find their number.

 

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

(ii) (ab) R (cd) ⇒ (cd) R (ab) for all (ab), (cd) ∈ N × N

 

 


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


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 R = {(xy) : xy ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.


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


Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B


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 ______.


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


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

R6 = {(a, b)/a ∈ N, a < 6 and b = 4}


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

R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}


Answer the following:

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


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


Multiple Choice Question :

Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to 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:

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 members of a family. The relation R defined by “aRb if a is not a sister of b”


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 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is transitive


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 symmetric


Is the following relation a function? Justify your answer

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


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 R3 = {(x, x) | x is a real number} is a relation. Then find domain and range of R3.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×