मराठी

Is the given relation a function? Give reasons for your answer. t = {(x, 3) | x is a real number - Mathematics

Advertisements
Advertisements

प्रश्न

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

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

बेरीज
Advertisements

उत्तर

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

Therefore, the domain element x is a real number.

Also, range has one number i.e., 3 in it.

Therefore, for every element in the domain has the image 3, it is a constant function.

A relation is said to be function if every element of one set has one and only one image in other set.

Hence, t is a function.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Relations and Functions - Exercise [पृष्ठ २८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
पाठ 2 Relations and Functions
Exercise | Q 10.(v) | पृष्ठ २८

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.


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


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.


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.


Determine the domain and range of the relation R defined by

(i) R = [(xx + 5): x ∈ (0, 1, 2, 3, 4, 5)]


Determine the domain and range of the relations:

(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and}  \left| a \right| \leq 3 \right\}\]

 


Define a relation R on the set N of natural number by R = {(xy) : y = x + 5, x is a natural number less than 4, xy ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or 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 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 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 R = [(xy) : xy ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.


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


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


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


R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 is


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


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

R2 = {(1, 5), (2, 4), (3, 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:

Show that the following is an equivalence relation

R in A = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}


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 :

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


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 A be the set consisting of all the female 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 equivalence


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


Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai


Choose the correct alternative:

Let R be the universal relation on a set X with more than one element. Then R is


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


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


If R = {(x, y): x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is ______.


Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×