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Consider the following properties:

  1. Reflexive
  2. Antisymmetric
  3. Symmetric

Let $A=\{a,b,c,d,e,f,g\}$ and $R=\{(a,a), (b,b), (c,d), (c,g), (d,g), (e,e), (f,f), (g,g)\}$ be a relation on $A$. Which of the following property (properties) is (are) satisfied by the relation $R$?

  1. Only $i$
  2. Only $iii$
  3. Both $i$ and $ii$
  4. $ii$ and not $i$
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2 Answers

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A={a,b,c,d,e,f,g}   and

R={(a,a),(b,b),(c,d),(c,g),(d,g),(e,e),(f,f),(g,g)} be a relation on A

R is not reflexive as neither  pair c,c not d,d is not here in R

R is not symmetric as c,d is there but d,c is not there in R

R is antisymmetric as if has no violation of property  that if a,b in R and b,a in R then a=b

either if condition is false in R or both if then are true

hence option D is right ans
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option d  

(c,c) missng not reflexive

(c,g) is there but not(g,c) not symetric

so simply OPTION D
Answer:

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