हिंदी

Determine the Domain and Range of the Relations:(I) R = {(A, B) : A ∈ N, A < 5, B = 4}

Advertisements
Advertisements

प्रश्न

Determine the domain and range of the relations:

(i) R = {(ab) : a ∈ N, a < 5, b = 4}

Advertisements

उत्तर

(i) = {(ab) : a ∈ N, a < 5, b = 4}
We have:
= 1, 2, 3, 4
= 4
R = {(1, 4), (2, 4), (3, 4), (4, 4)}
Domain (R) = {1, 2, 3, 4}
Range (R) = {4}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Relations - Exercise 2.3 [पृष्ठ २१]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 2 Relations
Exercise 2.3 | Q 10.1 | पृष्ठ २१

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?


If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.

(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.


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.


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 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


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 =


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


If the set A has p elements, B has q elements, then the number of elements in A × B 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, y + 4) = (1, 2) find the values of x and y


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

R1 = {(a, a2)/a is prime number less than 15}


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}


Write the relation in the Roster Form. State its domain and range

R6 = {(a, b)/a ∈ N, a < 6 and b = 4}


Write the relation in the Roster Form. State its domain and range

R7 = {(a, b)/a, b ∈ N, a + b = 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}      

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:

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


Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”


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”


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 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 symmetric


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


Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?


Choose the correct alternative:

The number of relations on a set containing 3 elements is


Choose the correct alternative:

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


Is the following relation a function? Justify your answer

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


Is the following relation a function? Justify your answer

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


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

s = {(n, n2) | n is a positive integer}


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

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


Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×