##<b>Unscramble the following examples</b>. The relations below are defined on the set $\m N=\{0,1,2,3,\ldots\}$. #$R_0=\{\}=\emptyset$ is$\ \neg$reflexive, irreflexive, symmetric, antisymmetric, asymmetric and transitive #$R_1=\{(x,y)\ |\ x=y\}$ is reflexive,$\ \neg$irreflexive, symmetric, antisymmetric,$\ \neg$asymmetric and transitive #$R_2=\{(x,y)\ |\ x\ne y\}$ is$\ \neg$reflexive, irreflexive, symmetric,$\ \neg$antisymmetric,$\ \neg$asymmetric and$\ \neg$transitive #$R_3=\{(x,y)\ |\ x\le y\}$ is reflexive,$\ \neg$irreflexive,$\ \neg$symmetric, antisymmetric,$\ \neg$asymmetric and transitive #$R_4=\{(x,y)\ |\ x<y\}$ is$\ \neg$reflexive, irreflexive,$\ \neg$symmetric, antisymmetric, asymmetric and transitive #$R_5=\{(x,y)\ |\ y=x+1\}$ is$\ \neg$reflexive, irreflexive,$\ \neg$symmetric, antisymmetric, asymmetric and$\ \neg$transitive #$R_6=\{(x,y)\ |\ y=x^2\}$ is$\ \neg$reflexive,$\ \neg$irreflexive,$\ \neg$symmetric, antisymmetric,$\ \neg$asymmetric and$\ \neg$transitive #$R_7=\m N\times\m N$ is reflexive,$\ \neg$irreflexive, symmetric,$\ \neg$antisymmetric,$\ \neg$asymmetric and transitive