Answer :

Given that, R = {(x, y): x N, y N, 2x + y = 41}


Now, 2x + y = 41


y = 41 - 2x (i)


Since x N, y N from (i) we get the relation


R = {(1,39),(2,37),(3,35),(4,33),(5,31),(6,29),(7,27),(8,25),


(9,23),(10,21),(11,19),(12,17),(13,15),(14,13),(15,11),


(16,9),(17,7),(18,5),(19,3),(20,1)}


Domain(R) ={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}


Range(R) ={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,


37,39}


R is not reflexive (1,1),(2,2)…(20,20) R


R is not symmetric (1,39) R but (39,1) R


R is not transitive (12,17),(17,7) R but (12,7) R


Hence, R is neither reflexive nor symmetric nor transitive.


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