Consider the preorder \\( P = Q = \underline{3} \\).

1) Let \\( f , g \\) be the monotone maps shown below:

![monotone maps](https://docs.google.com/drawings/d/e/2PACX-1vQGIFuhjduovYATNRvYUzuQez6ydFUdmaEkr8YkmdS4c0YyO4OnWTzzVZqSEdcxsQVm2uzTqqR2gYdI/pub?w=381&h=175)

Is it the case that \\(f\\) is left adjoint to \\(g\\)?

Check that for each \\( 1 \le p, q \le 3 \\), one has \\( f(p) \le q \text{ iff } p \le g(q) \\).

2) Let \\( f , g \\) be the monotone maps shown below:

![map 2](https://docs.google.com/drawings/d/e/2PACX-1vSE2cWf8muuJUKlfudgei-lWOvBAIAeuAs9XzN4xVM5hcyTNRR7kb_iSdhsGBfFHH_Z8r6Ww_mbdsuR/pub?w=381&h=175)

Is it the case that \\(f\\) is left adjoint to \\(g\\)?