GO Classes Set Theory And Algebra Practice Set 1 | Question: 2

Question

$$\begin{array}{l|llllll}
\textbf{Relations on}\; \mathbb{Z}: & \quad < & \qquad \leq & \qquad = & \qquad \mid & \qquad \nmid & \qquad \neq \\
\hline \hline \text{Reflexive} & \\
\text{Symmetric} & \\
\text{Transitive} &
\end{array}$$
Fill "Yes or No" in the above table.

Answer 1

$$\begin{array}{l|llllll}
\textbf{Relations on}\; \mathbb{Z}: & \quad < & \qquad \leq & \qquad = & \qquad \mid & \qquad \nmid & \qquad \neq \\
\hline \hline \text{Reflexive} & \quad \text{no} &\qquad \text{yes} & \qquad \text{yes} & \qquad \text{yes} &\qquad \text{no} & \qquad\text{no} \\
\text{Symmetric} & \quad \text{no} &\qquad \text{no} & \qquad \text{yes} & \qquad \text{no} &\qquad \text{no} & \qquad\text{yes}\\
\text{Transitive} & \quad \text{yes} &\qquad \text{yes} & \qquad \text{yes} & \qquad \text{yes} &\qquad \text{no} & \qquad\text{no}
\end{array}$$