English

Is the following relation a function? Justify your answer R2 = {(x, |x |) | x is a real number}

Advertisements
Advertisements

Question

Is the following relation a function? Justify your answer

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

Sum
Advertisements

Solution

R2 = {(x, |x |) / x ∈R}

For every x ∈ R there will be unique image as |x | ∈ R.

Therefore R2 is a function.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Relations and Functions - Solved Examples [Page 24]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 2 Relations and Functions
Solved Examples | Q 5.(ii) | Page 24

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 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.


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] and B = [3, 4]. Find the total number of relation 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.


Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(xy) : 3x − y = 0, where xy ∈ 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
(ab) R (cd) ⇔ a + d = b + c for all (ab), (cd) ∈ N × N
Show that:
(i) (ab) R (ab) for all (ab) ∈ N × N


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


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

 

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


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


If the set A has p elements, B has q elements, then the number of elements in A × B is


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


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

R4 = {(x, y)/y > x + 1, x = 1, 2 and y = 2, 4, 6}


Identify which of if the following relations are reflexive, symmetric, and transitive.

Relation Reflexive Symmetric Transitive
R = {(a, b) : a, b ∈ Z, a – b is an integer}      
R = {(a, b) : a, b ∈ N, a + b is even} x
R = {(a, b) : a, b ∈ N, a divides b}      
R = {(a, b) : a, b ∈ N, a2 – 4ab + 3b2 = 0}      
R = {(a, b) : a is sister of b and a, b ∈ G = Set of girls}      
R = {(a, b) : Line a is perpendicular to line b in a plane}      
R = {(a, b) : a, b ∈ R, a < b}      
R = {(a, b) : a, b ∈ R, a ≤ b3}      

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

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:

Show that the following is an equivalence relation

R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}


Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R2 = {(–1, 1)}


Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R3 = {(2, –1), (7, 7), (1, 3)}


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}


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:

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 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 equivalence


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


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 transitive


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 following relation a function? Justify your answer

R1 = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`


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

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


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×