मराठी

Let R Be a Relation on N Defined by X + 2y = 8. the Domain of R is (A) [2, 4, 8] (B) [2, 4, 6, 8] (C) [2, 4, 6] (D) [1, 2, 3, 4]

Advertisements
Advertisements

प्रश्न

Let R be a relation on N defined by x + 2y = 8. The domain of R is

पर्याय

  • (a) [2, 4, 8]

  • (b) [2, 4, 6, 8]

  • (c) [2, 4, 6]

  • (d) [1, 2, 3, 4]

     
MCQ
Advertisements

उत्तर

(c) {2, 4, 6}

x + 2y = 8
⇒ x = 8 -2y
For y = 1, x = 6
y = 2, x = 4
y = 3, x = 2
Then R = {(2,3),(4,2),(6,1)}
∴ Domain of R = {2,4,6}

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Relations - Exercise 2.5 [पृष्ठ २६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 2 Relations
Exercise 2.5 | Q 8 | पृष्ठ २६

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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


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.


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.


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

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


Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.

 

Determine the domain and range of the relation R defined by

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


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
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:

(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N

 

 


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


Let R = [(x, y) : x, y ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.


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


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


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

R2 = {(1, 5), (2, 4), (3, 6)}


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 reflexive


Answer the following:

Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.


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.


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}


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}


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 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 equivalence


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 equivalence


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:

The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one of the following is true?


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


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

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


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

g = `"n", 1/"n" |"n"` is a positive integer


Which statement defines a relation from set \(A\) to set \(B\)?


For \(A=\{-1,0,1\}\), which ordered pair is a remaining element of \(A\times A\) besides \((-1,0)\) and \((0,1)\)?


Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \((A\times B)\cap(A\times C)\)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×