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Argument: R2 is straight away eliminated. For R3, to satisfy Antisymmetric relation.. Say -2 and +2 satisfy it then +2 and -2 should not satisfy. But its not the case. Answer is given as C. Am I so blind that I couldn't figure out my mistake?

asked in Set Theory & Algebra by Loyal (2.7k points)   | 106 views

Answer is option D only , R3 is not an antisymetric relation .

4 Answers

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answer should be d). only R1 is partial order. clearly R3 is not satisfying criterion of antisymmetric relation.
answered by (199 points)  
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Option D will be right option.
answered by Boss (5.4k points)  
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Option D will be right option.

answered by Boss (5.4k points)  
r3 is not antisymmetric  here
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answer would be D:

R1 is definitely partial order set (>= is classic example of poset)

R2 is clearly not reflexive therefore not partial order set

coming to R3 : we have to check whether it is antisymmetric or not: i.e (aRb and bRa) implies a=b

suppose we take +3 and -3 now (3)2 <= (-3)and (-3)2 <= (3)2 implies that 3=-3 which is false therefore it is not antisymmetric in nature following not a partial order.

answered by Active (1.1k points)  

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