6 Show that the relation “greater thar" on the set of natural number

1.	6 Show that the relation “greater thar" on the set of natural numbers N, is transitive but is neither reflexive nor symmetric.
Answer» Basic Concept :- Reflexive :- RELATION is reflexive, If (a, a) ∈ R for every a ∈ A. Symmetric :- Relation is symmetric, If (a, B) ∈ R, then (b, a) ∈ R. Transitive :- Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R. Let's solve the PROBLEM now!! The given Relation R can be mathematically represent as $\rm :\longmapsto\:R \: = \{(a, b) : a > b \: where \: a, b \in \: N \}$ Reflexive :- $\rm :\longmapsto\:Let \: a \in \: N$ $\rm :\longmapsto\:We \: know, \: a \: = \: a$ $\rm :\implies\:a \: \cancel > \: a$ $\rm :\implies\:(a, a) \: \cancel \in \: R$ $\bf\implies \:R \: is \: not \: reflexive.$ Symmetric :- $\rm :\longmapsto\:Let \: a, b \: \in \: N \: such \: that \: (a, b) \in \: R$ $\rm :\implies\:a > b$ $\rm \: \cancel{\implies\:} \: b > a$ $\rm :\implies\:(a, b) \: \cancel \in \: R$ $\bf\implies \:R \: is \: not \: symmetric.$ Transitive :- $\rm :\longmapsto\:Let \: a,b,c \in \: N \: such \: that \: (a, b) \in \: R \: and \: (b, c) \in \: R$ $\rm :\longmapsto\:as \: (a, b) \in \: R \rm \: \implies\:a > b - - (1)$ $\rm :\longmapsto\:as \: (b, c) \in \: R \rm \: \implies\:b > c - - (2)$ From equation (1) and equation (2), we CONCLUDED $\rm :\longmapsto\:a > c$ $\rm :\implies\:(a, c) \in \: R$ $\bf\implies \:R \: is \: transitive.$