English

Select the correct answer from given alternative. If (x, y) ∈ R × R, then xy = x2 is a relation which is

Advertisements
Advertisements

Question

Select the correct answer from given alternative.

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

Options

  • Symmetric

  • Reflexive

  • Transitive

  • Equivalence

MCQ
Advertisements

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Sets and Relations - Miscellaneous Exercise 5.1 [Page 104]

APPEARS IN

Balbharati Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
Chapter 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (9) | Page 104

RELATED QUESTIONS

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 = {(x, x3) : x is a prime number less than 10}

 

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:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N


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

 

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


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.

 


Let A = [1, 2, 3, 5], B = [4, 6, 9] and R be a relation from A to B defined by R = {(x, y) : x − yis odd}. Write R in roster form. 


Let R be a relation on N defined by x + 2y = 8. The domain of R is


Let R be a relation from a set A to a set B, then


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 R is a relation on a finite set having n elements, then the number of relations on A is


If (x − 1, y + 4) = (1, 2) find the values of x and y


If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y


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

R6 = {(a, b)/a ∈ N, a < 6 and b = 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:

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 transitive


Answer the following:

Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.


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}


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 :

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 ________.


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


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 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 reflexive


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 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 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 equivalence


Choose the correct alternative:

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


Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.


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.

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


For a relation \(R\), the domain is the set of all:


If \(R\) is a relation from \(A\) to \(B\), what is its co-domain?


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×