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Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1 is parallel to I2}. What is the type of given relation?
- a)Reflexive relation
- b)Equivalence relation
- c)Symmetric relation
- d)Transitive relation
Correct answer is option 'B'. Can you explain this answer?
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Let I be a set of all lines in a XY plane and R be a relation in I def...
This is an equivalence relation. A relation R is said to be an equivalence relation when it is reflexive, transitive and symmetric.
Reflexive: We know that a line is always parallel to itself. This implies that I1 is parallel to I1 i.e. (I1, I2)∈R. Hence, it is a reflexive relation.
Symmetric: Now if a line I1 || I2 then the line I2 || I1. Therefore, (I1, I2)∈R implies that (I2, I1)∈R. Hence, it is a symmetric relation.
Transitive: If two lines (I1, I3) are parallel to a third line (I2) then they will be parallel to each other i.e. if (I1, I2) ∈R and (I2, I3) ∈R implies that (I1, I3) ∈R.
Reflexive: We know that a line is always parallel to itself. This implies that I1 is parallel to I1 i.e. (I1, I2)∈R. Hence, it is a reflexive relation.
Symmetric: Now if a line I1 || I2 then the line I2 || I1. Therefore, (I1, I2)∈R implies that (I2, I1)∈R. Hence, it is a symmetric relation.
Transitive: If two lines (I1, I3) are parallel to a third line (I2) then they will be parallel to each other i.e. if (I1, I2) ∈R and (I2, I3) ∈R implies that (I1, I3) ∈R.
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Let I be a set of all lines in a XY plane and R be a relation in I def...
Equivalence relation
An equivalence relation is a relation that satisfies three properties: reflexivity, symmetry, and transitivity.
Reflexive relation
A reflexive relation is a relation where every element is related to itself. In this case, the relation R defined as R = {(I1, I2):I1 is parallel to I2} is not reflexive because a line cannot be considered parallel to itself.
Symmetric relation
A symmetric relation is a relation where if (a, b) is in the relation, then (b, a) is also in the relation. In this case, the relation R defined as R = {(I1, I2):I1 is parallel to I2} is not symmetric because if line I1 is parallel to line I2, it does not necessarily mean that line I2 is parallel to line I1.
Transitive relation
A transitive relation is a relation where if (a, b) and (b, c) are in the relation, then (a, c) is also in the relation. In this case, the relation R defined as R = {(I1, I2):I1 is parallel to I2} is transitive because if line I1 is parallel to line I2, and line I2 is parallel to line I3, then it follows that line I1 is parallel to line I3. Therefore, it satisfies the transitive property.
Equivalence relation
To be an equivalence relation, a relation must satisfy all three properties: reflexivity, symmetry, and transitivity. Since the given relation R satisfies the transitive property, it can be considered an equivalence relation.
Therefore, the correct answer is option 'B' - Equivalence relation.
An equivalence relation is a relation that satisfies three properties: reflexivity, symmetry, and transitivity.
Reflexive relation
A reflexive relation is a relation where every element is related to itself. In this case, the relation R defined as R = {(I1, I2):I1 is parallel to I2} is not reflexive because a line cannot be considered parallel to itself.
Symmetric relation
A symmetric relation is a relation where if (a, b) is in the relation, then (b, a) is also in the relation. In this case, the relation R defined as R = {(I1, I2):I1 is parallel to I2} is not symmetric because if line I1 is parallel to line I2, it does not necessarily mean that line I2 is parallel to line I1.
Transitive relation
A transitive relation is a relation where if (a, b) and (b, c) are in the relation, then (a, c) is also in the relation. In this case, the relation R defined as R = {(I1, I2):I1 is parallel to I2} is transitive because if line I1 is parallel to line I2, and line I2 is parallel to line I3, then it follows that line I1 is parallel to line I3. Therefore, it satisfies the transitive property.
Equivalence relation
To be an equivalence relation, a relation must satisfy all three properties: reflexivity, symmetry, and transitivity. Since the given relation R satisfies the transitive property, it can be considered an equivalence relation.
Therefore, the correct answer is option 'B' - Equivalence relation.
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Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer?
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Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer?.
Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1is parallel to I2}. What is the type of given relation?a)Reflexive relationb)Equivalence relationc)Symmetric relationd)Transitive relationCorrect answer is option 'B'. Can you explain this answer?.
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