$(12$ pts$)$ Determine whether the following binary relation is:

$(1)$ reflexive, $(2)$ symmetric, $(3)$ antisymmetric, $(4)$ transitive.

No justifications needed.

a$)(4$ pts$)$ The relation $R$ on $Z$ where aRb means $a=b.$

Circle your answers.

b$)(4$ pts$)$ The relation $R$ on the set of all people where aRb means that $a$ is not taller than $b.$

Circle your answers.

c$)(4$ pts$)$ If $M_R=\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& 1& 1& 0\\ 1& 1& 1& 0\\ 0& 0& 0& 1\end{array}\right],$

determine if $R$ is: $($a$)$ reflexive $($b$)$ symmetric $($c$)$ antisymmetric $($d$)$ transitive.

Circle your answers.