Linked and Independent Sets

For $M \subseteq \mathbb{N}^*$ with $|M| = n \ge 5$: if $M$ contains four distinct elements $a, b, c, d$ with $a + b = c + d$, call $M$ linked and $\{a,b,c,d\}$ a linked subset; otherwise call $M$ independent.

1. Are $\{2,4,6,8,10\}$ and $\{1,2,3,5,8\}$ linked or independent? For linked ones, list all linked subsets. 2. Suppose $M = \{a_1 < \cdots < a_5\}$ is linked, and every pair $\{a_i, a_j\}$ is contained in some linked subset of $M$. Prove that $a_1, \dots, a_5$ form an arithmetic progression. 3. If $M$ is independent, prove that some $x \in M$ satisfies $x > \dfrac{n^2 - n + 9}{4}$.