Let and, for each , define…

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

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.