A graph $L_n$ has vertices $V=\{l_1,l_2,\dotsc,l_n\}\cup\{r_1,r_2,\dotsc,r_n\}$ and edges $E=\{(l_i,r_j): i \ge j\}$ .
Which of these graphs $L_1$, $L_2$, etc. are planar and which are not? For those that are planar, give an appropriate depiction (scheme) and for the others write the proof.