English

Answer the following: Determine the domain and range of the following relation. R = {(a, b)/a ∈ N, a < 5, b = 4}

Advertisements
Advertisements

Question

Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}

Sum
Advertisements

Solution

R = {(a, b)/a ∈ N, a < 5, b = 4}

Domain of R = {a/a ∈ N, a < 5}

={1, 2, 3, 4}

Range of R = {b/b = 4}

= {4}

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Sets and Relations - Miscellaneous Exercise 5.2 [Page 105]

APPEARS IN

Balbharati Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
Chapter 5 Sets and Relations
Miscellaneous Exercise 5.2 | Q II. (7) (i) | Page 105

RELATED QUESTIONS

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?


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

  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.

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


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.


Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?

f is a relation from A to B

Justify your answer in case.


Find the inverse relation R−1 in each of the cases:

(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}


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

 

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

 

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 and (b, c) ∈ R implies (a, c) ∈ R

Justify your answer in case.


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?


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
Show that:

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

 

 


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


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


Let A = [1, 2, 3], B = [1, 3, 5]. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R−1 is


A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is


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


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


If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B


Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∩ C) = (A × B) ∩ (A × C)


Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)


Select the correct answer from given alternative.

The relation ">" in the set of N (Natural number) 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)}


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

R4 = {(4, 2), (2, 6), (5, 1), (2, 4)}


Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}


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?

R4 = {(7, –1), (0, 3), (3, 3), (0, 7)}


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:

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:

On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”


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 reflexive


In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation


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?


Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×