#I cant understand why it is not transitive

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spare verge
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Well why do you think it's transitive then?

dreamy tangle
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R={(1,2),(1,3),(2,1),(2,3),(3,1),(3,2)
then (2,1) -> (1,3) -> (2,3)

spare verge
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Ok, is that the only choice of x,y,z you can make?

dreamy tangle
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(1,2 ), (2,3),(1,3)

spare verge
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what happens if you take (1,2) and (2,1)?

dreamy tangle
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mm we cant call it transitive for these?

spare verge
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yes, you've found a pair of elements that make it fail

dreamy tangle
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okay

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so it should be true for all possible elements?

spare verge
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clearly not

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we just said it was false

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1 does not equal 2, 2 does not equal 1, but 1 equals 1

dreamy tangle
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like all of the possible one
even one failed makes it not transititve?

spare verge
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yes

dreamy tangle
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oo okay

spare verge
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transitive is, for all x,y,z such that (x,y) and (y,z) are in R, then (x,z) is in R

dreamy tangle
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okay thennn

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and same for symmetric and reflexive?

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these should all have all the posibilities?

spare verge
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yes

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for all x, (x,x) is in R
for all x,y such that (x,y) is in R, (y,x) is in R

dreamy tangle
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'all'
correct
now i understood the whole topic

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aah thank you so much
i was getting so confused with all the terms