Generalizing the two examples given above, answer the following questions using the meet $$ and join $$ operations $($the meet $ab$ is the greatest element below a and $b$; the join $ab$ is the least element above a and $b)$:

Given two objects $o_1,o_2$ at different security levels $s_1$ and $s_2$ what is the maximal security level $L_{\text{m}\text{a}\text{x}}$ a subject $u$ can have to be allowed to write both objects?

Given two subjects $u_1,u_2$ at different security levels $s_1$ and $s_2,$ what is the minimal security level $L_{\text{m}\text{i}\text{n}}$ an object $o$ must have so that both subjects can still write on it$?$