Let S={1,2,3,4,5,6}. A relation R is defined on S by
R={(a,b)∈S×S∣a+b is divisible by 3}.
Study this relation and answer the following:
a. (i) List all ordered pairs belonging to R.
b. (ii) Find the domain and the range of R.
c. (iii) Prove that R is symmetric.
d. (iv) Determine, with proof, whether R is (a) reflexive and (b) transitive.