Symmetric and antisymmetric relations
6.1
A relation R on a set A is called symmetric if aRb ? bRa for
all a,b?A; R is antisymmetric if aRb ? a?b ? bRa for all a,b?A.
Symmetric? Antisymmetric?
R1={(a,b) | a?b}
R2={(a,b) | a>b}
R3={(a,b) | a=b or a=-b}
R4={(a,b) | a=b}
R5={(a,b) | a=b+1}
R6={(a,b) | a+b ?3}
No
No
Yes
Yes
No
Yes
Yes
Yes
No
Yes
Yes
No
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