The document discusses antisymmetric and symmetric relations. It provides the example of the less than or equal to relation (<=) on real numbers as an antisymmetric relation, since if a <= b and b <= a, then a must equal b. The example given in the question of comparing real numbers to exponentials is shown not to be antisymmetric. A symmetric relation is defined such that if a relates to b, then b also relates to a, with examples given as equivalence relations where a relates to b if and only if they are equal, or a relation where the absolute value of the difference between a and b is a constant.
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Antisymmetric Real numbers, xRy off x is less than or equal to 2^y..pdf
1. Antisymmetric? Real numbers, xRy off x is less than or equal to 2^y. I could not find an
example of symmetry?
Solution
Anti symmetric means:if aRb and bRa then a=b. An example of anti symmetric
relation on real numbers is <=(less than equal). ie if (a <= b) and (b <= a). Then a=b. The
example you have given is not antisymmetric. eq 4 <= (2^5)=32 and 5<= 2^4=16. But 4 not
equal to 5. Symmetric: aRb then bRa. standard examples for symmetric relations are some
equivalence relations eg. aRb iff a=b. So, if aRb then bRa as a=b then b=a. or other relations can
be |a-b|=constant. This is also symmetric.
