Let and let a relation on be given in roster form as R=…
MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Let A={1,2,3,4} and let a relation R on A be given in roster form as
R={(1,1),(2,2),(3,3),(1,2),(2,1),(3,2),(2,3)}.
(i) State the definitions of a reflexive relation, a symmetric relation and a transitive relation on a finite set.
(ii) Using the above definitions, examine whether the relation R is
(a) reflexive,
(b) symmetric,
(c) transitive,
justifying every conclusion by referring to specific ordered pairs that belong or do not belong to R.