I can extract and solve the mathematical questions from the image you uploaded. Here is the breakdown of the problems and the steps I will take to solve them:

Question 1: Sublattices of $L$

Determine which of the given subsets $L_1, L_2, L_3, L_4$ are sublattices of $L$, and provide justification for each. Verify the closure under meet ($\land$) and join ($\lor$) for each subset.

Question 2: Complements

Find the complements of elements $a, b, c$ if they exist. Complements are determined if: $x \lor y = 1 \quad \text{and} \quad x \land y = 0$ for elements $x, y$.

Question 3: Hasse Diagram of $D_{36}$

1. Draw the Hasse diagram of the poset $D_{36}$, which is the lattice of divisors of $36$ under the partial order of divisibility.
2. Find complements of $2$ and $9$, if they exist.
3. Determine whether $D_{36}$ is complemented.

Question 4: Poset Properties

For the given poset $P$, identify:

1. Maximal and minimal elements.
2. The least upper bound ($\sup$) and greatest lower bound ($\inf$) for subsets $\{2,3\}, \{5,3\}$, if they exist.

Would you like me to start solving these questions step-by-step, or focus on specific parts? Let me know!