Question

Let `S` be the set of all sets and let `R={(A,B):A sub B}`,i.e., . `A` is a proper subset of `B`. Show that `R` is (i) Transitive (ii) Not reflexive (iii) not symmetric.

Answer 1

(i) `( sub B and B sub C )implies ( A sub C).` SO ,R is transitive
(ii) Clearly `A sub C` is not ture .SO ,R is not reflexive .
(iii) if `A sub B ` then `B sub C` is not true .SO .R is not symmetric .