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Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.
I. {(1,1), (2,2), (3,3)}
II. {(1,1), (2,2)}
III. {(1,1), (2,2), (3,3), (1,2)}
Which of the above correctly represent(s) the smallest reflexive closure of R?
- a)Both I and III
- b)Only I
- c)Only III
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (...
The common mistake here is to pick both I and III as the answer, which is wrong. Why? Because first of all in order for a relation T (say) to be reflexive closure of a relation R, then firstly T must be a superset of R, and only then we think about reflexivity, So I is actually a subset of R and thus cannot be the reflexive closure of R. II does not contain (3,3) and therefore is not reflexive, So the correct answer is choice (c).
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Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (...
The reflexive closure of a relation R on a set A is the smallest reflexive relation on A that contains R. In other words, it is the relation obtained by adding all the missing reflexive pairs to R.
To find the reflexive closure of R, we need to add the missing reflexive pairs to R. In this case, R is already reflexive for the elements 1, 2, and 3, but it is missing the pair (2,1) to make it reflexive for the element 1. So, the reflexive closure of R is obtained by adding (2,1) to R.
Now let's consider the given relations and check if they represent the reflexive closure of R:
I. {(1,1), (2,2), (3,3)}
This relation includes all the reflexive pairs for the elements 1, 2, and 3, but it does not include the pair (2,1). Therefore, it is not the reflexive closure of R.
II. {(1,1), (2,2)}
This relation includes the reflexive pairs for the elements 1 and 2, but it does not include the pairs (3,3) and (2,1). Therefore, it is not the reflexive closure of R.
III. {(1,1), (2,2), (3,3), (1,2)}
This relation includes all the reflexive pairs for the elements 1, 2, and 3, as well as the pair (1,2). Therefore, it is the reflexive closure of R.
Therefore, the correct answer is option D, None of these.
To find the reflexive closure of R, we need to add the missing reflexive pairs to R. In this case, R is already reflexive for the elements 1, 2, and 3, but it is missing the pair (2,1) to make it reflexive for the element 1. So, the reflexive closure of R is obtained by adding (2,1) to R.
Now let's consider the given relations and check if they represent the reflexive closure of R:
I. {(1,1), (2,2), (3,3)}
This relation includes all the reflexive pairs for the elements 1, 2, and 3, but it does not include the pair (2,1). Therefore, it is not the reflexive closure of R.
II. {(1,1), (2,2)}
This relation includes the reflexive pairs for the elements 1 and 2, but it does not include the pairs (3,3) and (2,1). Therefore, it is not the reflexive closure of R.
III. {(1,1), (2,2), (3,3), (1,2)}
This relation includes all the reflexive pairs for the elements 1, 2, and 3, as well as the pair (1,2). Therefore, it is the reflexive closure of R.
Therefore, the correct answer is option D, None of these.
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Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer?
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Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let R be a relation on the set A = {1, 2, 3}, such that R = {(1,1), (2,2), (3,3), (1,2)}. Now consider the following relations.I. {(1,1), (2,2), (3,3)}II. {(1,1), (2,2)}III. {(1,1), (2,2), (3,3), (1,2)}Which of the above correctly represent(s) the smallest reflexive closure of R?a)Both I and IIIb)Only Ic)Only IIId)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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