Question

1. (15) Characterize the following relations in terms of whether they are reflexive, irreflexive, symmetric, anti- symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. a. R CRX R with R = {(x,y)|x<y>} b. RCRXR with R= {(x, y)|x3 = y3} C. RSRXR with R = {(x, y) x2 + y2}

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Answer 1

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RCRXR Wwith R feive 2 r2 Hence, nat flesive (o4 R Herve, e sive ii) ymmetric itn then means that ,) ER then Hence, not ymmetic Amtinymmetic i net les than a then then Lya R Hence, anti ym etric

v) Transitive then Hane y)eR (yeR then R t i toanaitive 2 Thiu lation nat aun eauivelence lahion hecause it net eive ic is RERXR with R Refleive R Hence, fherive Yelalion

() Tefiesve t is efleseive AS inpleive net C) Symetic 3 then ta-j then y)R o,ymmeticlation Anti mmcric )ER then ly/) eR whn oney Hence, anti- suymetic ranitive then Hence, transitive uivalence lati on t i feuve, 3mmetne , thansitue as

RCRAR with R- ECa) () eive as Nonot ferive feemive I (24)R y mmetnic y) R then , also e R iAntiay metic than ymR uye R so, nat anti-mmetic Transitive Hence 4 R 4.30 R 2) (211) Not an eaivalence lation then (a1) ho Cl,1) ih elation No, not tangve