Relations - Set Theory

Question

Let A = {1,2,3 }

R= {(1,1)(2,2)(3,2)(1,2)(2,3)}

S= {(1,1)(2,2)(3,3)(2,3)(3,2)}

Which of the following ARE correct Justify Each Option ( for my understanding )

• R is not reflexive (3,3) is missing
• R is not anti symmetric (3,3) is missing
• R INTERSECTION S is an Equivalence Relation
• R is an equivalence Relation where as  R UNION S is Not.

1. Pls tell me one Anti-Symmetric Relation other than diagonal pairs

Comments

Sir , Is this explanation correct ?

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No. Avoid that book.

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Thanx :D

Answer 1

R is not reflexive ->reason given by you

R is not anti symmetric  as it have (2,3)and {3,2} .R intersection S not equivalence--->as it is not reflexive(as {3,3} missing.

R is not equivalence relation {3,3} missing

R U S not equivalence---{2,1} missing

Comments

R not reflexive...hence not equivalence hence R inter S not  equivalence

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Sir, can u pls tell me ONE anti symetric relation other than diagonal pairs
 

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I also uploaded an image...
How do you account to it ?

Answer 2

Main Anti symmetric condition is that aRb and bRa then a==b.It is publically known but it is important that no below element should be present as (1,2) (2,1).Such pairs voileted the condition of the Anti Symmetric.