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Select the correct answer from given alternative. If (x, y) ∈ R × R, then xy = x2 is a relation which is - Mathematics and Statistics

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प्रश्न

Select the correct answer from given alternative.

If (x, y) ∈ R × R, then xy = x2 is a relation which is

विकल्प

  • Symmetric

  • Reflexive

  • Transitive

  • Equivalence

MCQ
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उत्तर

If (x, y) ∈ R × R, then xy = x2 is a relation which is Equivalence

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Sets and Relations - Miscellaneous Exercise 5.1 [पृष्ठ १०४]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 5 Sets and Relations
Miscellaneous Exercise 5.1 | Q I. (9) | 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.


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


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 = (xyz) and B = (ab). Find the total number of relations 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 A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by {(ab) : ab ∈ A, b is exactly divisible by a}

(i) Writer R in roster form
(ii) Find the domain of R
(ii) Find the range of R. 


Let R be a relation on N × N defined by
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Write the relation in the Roster Form. State its domain and range

R7 = {(a, b)/a, b ∈ N, a + b = 6}


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Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}


Answer the following:

Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}


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 symmentric


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.


Represent the given relation by
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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 ________.


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


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


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

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

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Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.


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