R1) Reflexive : a+a=2a always even
Symmetric: either (a,b) both must be odd or both must be even to have sum as even
therefore, if(a,b) then definately (b,a)
Transitive: if(a,b) and (b,c) , then both of them must be even pairs or odd pairs and therefore (a,c) is even
R2) Reflexive : a+a=2a cant be odd ever
R3) Reflexive: a.a>0
Symmetric: if a,b>0 then both must be +ve or -ve, which means b.a >0 also exists
Transitive : if a.b>0 and b.c>0 then to have b as same number, both pairs must be +ve or -ve which implies a.c>0
R4) Reflexive: |a-a|<=2
Symmetric: if |a-b|<=2 definately |b-a|<=2 when a,b are natural numbers
Transitive: |a-b|<=2 and |b-c|<=2, doesnt imply |a-c|<=2
ex: |4-2|<=2 and |2-0|<=2 , but |4-0|>2 ,
hence, R2 and R4 are not equivalence
B)