हिंदी

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 function from A to B Justify your answer in case.

Advertisements
Advertisements

प्रश्न

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 function from A to B

Justify your answer in case.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

Since (2, 9), (2, 11)  f i.e., f contains two ordered pairs with the same first element. Hence, f is not a function from A to B.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Relations and Functions - Miscellaneous Exercise [पृष्ठ ४०]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 2 Relations and Functions
Miscellaneous Exercise | Q 10 (ii) | पृष्ठ ४०

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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.

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.


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.

 

Determine the domain and range of the relations:

(i) R = {(ab) : a ∈ N, a < 5, b = 4}


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 implies (b, a) ∈ 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?


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 R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =


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


A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?

 

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


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


If P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P


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

R3 = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}


Select the correct answer from given alternative.

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


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:

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


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.


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)}


Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}


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 :

The range of the relation R = {(x, x2) | x is a prime number less than 13} 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 ________.


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”


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 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 symmetric


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?


Choose the correct alternative:

The number of relations on a set containing 3 elements is


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

h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×