Let R be the relation defined on the set of natural number N as R={(x,y):x,ybelong to N, 2x+y=41}.Find the domain and range of R.also verify whether R is (a) reflexive (b). Symmetric (c)transitive.

2x+y=41y=41-2xAs yNso,41-2x1-2x-40x20So, domain is first 20 natural numbers.2x=41-yx=41-y2As xN41-y2141-y2y39So, range is First 39 natural numbers.For Reflexive :-a,aR2a+a=413a=41 , falseHence , R is not reflexive.For symmetric:-a,bR 2a+b=412b+a=41 , falseso, b,aRHence R is not symmetric.For transistive :-a,b  R and b,cR2a+b=41   and   2b+c=41but 2a+c41so , a,cRHence , R is not transistive.

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