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Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)} be a relation on A. Here, R is
  • a)
    Transitive
  • b)
    anti – symmetric
  • c)
    symmetric
  • d)
    reflexive
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)} be a relati...
Any relation R is reflexive if fx Rx for all x ∈ R. Here ,(a, a), (b, b), (c, c) ∈ R. Therefore , R is reflexive.
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Most Upvoted Answer
Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)} be a relati...
FOR BEING SYMMETRY
At least one such order pair should be found (a, a) or (b, b)
like that
In given relation, (a, a) or (b, b) is found, then it is reflexive.
FOR BEING SYMMETRY
Every relation must have such pair of order pair
for (a, b) must be (b, a)
For (c, a) must be in relation (a, c) like that
But we can see in question for (b, c) there is no (c, b)
That's why that is not symmetry
FOR BEING TRANSITIVE
If any relation contain (a,b) and (b, c) then for being transitive (a, c) must be relation.
Note if any relation contain (a, b) but does not contain either (a, c) or (b, c) then they are transitive
In question, (b, c) and also (b, b) but does not contain (c, b)
So it is not transitive
Note : (a, b) is not equal to (b, a)
Read it care you will understood completely
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Community Answer
Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)} be a relati...
Both reflexive and transitive
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Let A = {a, b, c} and R = {(a, a), (b, b), (c, c), (b, c)} be a relation on A. Here, R isa)Transitiveb)anti – symmetricc)symmetricd)reflexiveCorrect answer is option 'D'. Can you explain this answer?
Question Description
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