Consider the set

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the set

B=\{a,b,c,d\}

. Design a relation

R

B

that satisfies all the conditions given below and justify each point with explicit reasoning. (a)

R

contains exactly

6

ordered pairs. (b)

R

is symmetric. (c)

R

is neither reflexive nor transitive. List the ordered pairs of

R

and then, for each of the three properties above, provide a clear argument showing why the relation satisfies (b) and fails (c) and (a) is met.