Show that the relation "less than or equal to" on the set of integers

1.	Show that the relation "less than or equal to" on the set of integers Z, is reflexive and transitivebut not 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. If relation is reflexive, symmetric and transitive Let's solve the problem now!! Here, Relation, R mathematically represented as $\rm :\longmapsto\:R \: = \{(a, b) : a \leqslant b \: where \: a, b \: \in \: Z \}$ Reflexive :- $\rm :\longmapsto\:Let \: a \: \in \: Z$ $\rm :\longmapsto\:We\:know,\: a = a$ $\rm :\longmapsto\:(a, a) \in \: R$ $\bf\implies \:R \: is \: reflexive$ Symmetric :- $\rm :\longmapsto\:Let \: a, b \in \: Z \: such \: that \: (a, b) \in \: R$ $\rm :\implies\:a \leqslant b$ $\rm : \cancel {\implies} \: \: b \leqslant a$ $\rm :\implies\:(b, a) \: \cancel\in \: R$ $\bf\implies \:R \: is \: not \: symmetric$ Transitive :- $\rm :\longmapsto\:Let \: a, b, c \in \: Z \: such \: that(a, b) \in \: R \: and \: (b, c) \in \: R$ $\rm :\longmapsto\:as \: (a, b) \in \: R\rm :\implies\:a \leqslant b - - (1)$ $\rm :\longmapsto\:as \: (b, c) \in \: R \rm \: \implies\:b \leqslant c - - (2)$ From equation (1) and equation (2), we concluded that $\rm :\longmapsto\:a \leqslant c$ $\rm :\implies\:(a, c) \in \: R$ $\bf\implies \:R \: is \: trasitive.$