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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from given alternative. Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.

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प्रश्न

Select the correct answer from given alternative.

Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.

पर्याय

  • reflexive

  • symmetric

  • transitive

  • none of these

MCQ
रिकाम्या जागा भरा
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उत्तर

None of these.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Sets and Relations - Miscellaneous Exercise 5.1 [पृष्ठ १०४]

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बालभारती Mathematics and Statistics (Arts and Science) Part 2 [English] Standard 11 Maharashtra State Board
पाठ 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (6) | पृष्ठ १०४

संबंधित प्रश्‍न

Let A = {1, 2, 3, …, 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain 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.

Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}.


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.


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.

 

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 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 and (b, c) ∈ R implies (a, c) ∈ R

Justify your answer in case.


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:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N


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

(iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ∈ N × N

 

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


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


If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is


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

R2 = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`


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}


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| ≥ 0}


Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R


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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 :

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 ________.


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 transitive


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 transitive


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 reflexive


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 symmetric


Is the following relation a function? Justify your answer

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


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.

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


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(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.


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.


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


A function from set \(A\) to set \(B\) is a relation in which:


For two non-empty sets \(A\) and \(B\), which expression gives their Cartesian product?


For a relation \(R\), the domain is the set of all:


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