AI Tutor
Back to Properties of relations

Exercise B

Avg difficulty 3.0

Show that a relation can be both symmetric and anti-symmetric by giving an interpretation that makes both of the following sentences true:

∀x∀y(R(x,y)→R(y,x))\displaystyle\forall x\forall y(R(x,y)\rightarrow R(y,x)) ∀x∀y((R(x,y)∧R(y,x))→x=y)\displaystyle\forall x\forall y((R(x,y)\wedge R(y,x))\rightarrow x=y)

Magnus et al., forall x: Calgary, Interpretations, Properties of relations, Exercise B

AI Tutor

Adapted from forall x: Calgary © 2025 P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach. Licensed under CC BY 4.0. Source: forall x: Calgary. Imported at revision ec34df8.