Find eight different relations on Z, one for each of the following eight options

Question

Find eight different relations on Z, one for each of the following eight options Reflexive, symmetric, anti transitive Reflexive, symmetric, but not transitive Reflexive and transitive. Inn not symmetric Symmetric and transitive, but not reflexive Reflexive, hut neither symmetric nor transitive Symmetric, hut neither reflexive nor transitive Transitive, but neither reflexive nor symmetric.

Explanation / Answer

1)R={(x,y)|x-y is divisible by 2,x,y belongs to Z} 2)R={(x,y)|x=y or x-y is not divisible by 3} 3)R={(x,y)|x-y>=0} 4)R={(x,y)x-y is not equal to 0} 5)R={(x,y)|x>=y or x-y is not divisible by 3} ot transistive because (2,4)and (4,8) is in R but (2,8) is not 6)R={(x,y)| x-y is not divisible by 3} 7)R={(x,y)|x>y and x divides y}

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