Each equivalence class is a set of points $($x$,$ y$)$ on the plane. Geometrically, what is the equivalence class

$[(1,0)]?$

Exercise $3\mathrm{.}2.[10$pts$]$ Consider a relation R on A $=$ R $\backslash$times R defined by:

$($a$,$ b$)$ R$($s$,$ t$)$ a$2+$ b$2<=$ s$2+$ t$2.$

Is it $($a$)$ reflexive, $($b$)$ anti$-$symmetric, $($c$)$ transitive? Explain!

Exercise $3\mathrm{.}3.[10$pts$]$ Consider a relation R on A $=\{$a$,$ b$,$ c$,$ d$\}$ defined by the arrow$-$diagrama b c d

Is it an order relation? Is it total? Explain!

Exercise $3\mathrm{.}4.[+2$pts$]$ A binary relation R is called asymmetric if a R b $$ b R a for every a$,$ b in A$.$

$($a$)$ Draw the arrow$-$diagram of a relation on the set A $=\{1,2\},$ which is antisymmetric, but not

asymmetric.

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