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Choose the correct alternative: Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integ

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प्रश्न

Choose the correct alternative:

Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?

विकल्प

  • T is an equivalence relation but S is not an equivalence relation

  • Neither S nor T is an equivalence relation

  • Both S and T are equivalence relation

  • S is an equivalence relation but T is not an equivalence relation.

MCQ
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उत्तर

T is an equivalence relation but S is not an equivalence relation

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets, Relations and Functions - Exercise 1.5 [पृष्ठ ४६]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 1 Sets, Relations and Functions
Exercise 1.5 | Q 5 | पृष्ठ ४६

संबंधित प्रश्न

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 relation from A to B

Justify your answer in case.


Determine the domain and range of the relations:

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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.


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(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


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Relation Reflexive Symmetric Transitive
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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

R3 = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}


Answer the following:

Determine the domain and range of the following relation.

R = {(a, b)/a ∈ N, a < 5, b = 4}


Answer the following:

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


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f is a function from A to B

Justify your answer in case.


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


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