Multiple choice

Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}.

Which one of the following is TRUE?

  1. R is symmetric but NOT antisymmetric

  2. R is NOT symmetric but antisymmetric

  3. R is both symmetric and antisymmetric

  4. R is neither symmetric nor antisymmetric
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For symmetry: if (a,b)∈R then (b,a)∈R must hold. Here (x,y)∈R but (y,x)∉R, so NOT symmetric. For antisymmetry: if (a,b)∈R and (b,a)∈R then a=b must hold. Here (z,x)∈R and (x,z)∈R but z≠x, so NOT antisymmetric. R is neither symmetric nor antisymmetric.

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