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 - Maths - Relations and Functions

Question

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

Rishabh Mittal · Accepted Answer

2x+y=41y=41-2xAs y∈Nso,41-2x≥1-2x≥-40x≤20So, domain is first 20 natural numbers
2x=41-yx=41-y2As x∈N41-y2≥141-y≥2y≤39So, range is First 39 natural numbers
For Reflexive :-a,a∈R2a+a=413a=41 , falseHence , R is not reflexive
For symmetric:-a,b∈R 2a+b=412b+a=41 , falseso, b,a∉RHence R is not symmetric
For transistive :-a,b ∈ R and b,c∈R2a+b=41   and   2b+c=41but 2a+c≠41so , a,c∉RHence , R is not transistive

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.