# DM - Functions & Relations -Q14

+1 vote

Let be the set of all propositions generated by and (Where and are Two Propositions) using at most one of the following logical operations : , Where are NAND and NOR operators respectively.

i.e.

A Relation is defined on such that   is Tautology.

The relation R is

A. An equivalence relation

B. Not an equivalence relation because R is Not transitive.

C. A partial order relation

D. Not a partial order relation because R is Not anti-symmetric.

reshown 6 days ago

R is reflexive because $X \rightarrow X$  is always a Tautology. $X \rightarrow X = X + X' =1$
R is antisymmetric. $xRy$ and $yRx$  implies $x \equiv y$ . Since, no two elements in the set L are equivalent so R is antisymmetric.
R is transitive because Implication operation is Transitive. $(x \rightarrow y ) \wedge (y \rightarrow z ) \rightarrow (x \rightarrow z )$