Mathematics

Problem

Let

R=\{(1,2),(2,3),(3,4)\}

and, for each

k\in\{1,2,3,4\}

, define

S_k=\{(1,2),(2,3),(3,k),(k,4)\}

. a. Determine all value(s) of

k

for which

R

is a subrelation of

S_k

. Show your reasoning briefly. b. For the value(s) of

k

obtained in part (i), state whether

S_k

is also a subrelation of

R

, and justify your answer with a short explanation.