Let . A relation is defined on by R= (a,b) S S a+b is divisible by 3 . Study this…

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

S=\{1,2,3,4,5,6\}

. A relation

R

is defined on

S

R=\{(a,b)\in S\times S\mid a+b \text{ is divisible by } 3\}.

Study this relation and answer the following: (i) List all ordered pairs belonging to

R

. (ii) Find the domain and the range of

R

. (iii) Prove that

R

is symmetric. (iv) Determine, with proof, whether

R

is (a) reflexive and (b) transitive.