monochromatic copy of $K^{v(H)}_{v(H)}(s)$, which gives a copy of $H(s)$ in $G$. $\square$

[**(Squeeze Theorem)**]{} Let $H$ be any hypergraph. If there exists a hypergraph $H^{\prime}$ and integer $s\geq 2$ such that $H^{\prime}\subseteq H\subseteq H^{\prime}(s)$ then $\pi(H)=\pi(H^{\prime})$.

[**Proof:**]{} One needs only observe that for any hypergraphs $H_{1}\subseteq H_{2}\subseteq H_{3}$ that $\pi(H_{1})\leq \pi(H_{2})\leq \pi(H_{3})$. If $H_{3}=H_{1}(s)$ for some $s\geq 2$ then $\pi(H_{1})=\pi(H_{3})$ by the previous theorem. $\square$

Turán Densities of $\{1,2\}$-hypergraphs
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In this section we will determine the Turán density for any hypergraph $H$ with $R(H)=\{1,2\}$. We begin with the following more general result.

Let $H=H^{1}\cup H^{k}$ be a hypergraph with $R(H)=\{1,k\}$ and $E(H^{1})=V(H^{k})$. Then $$\pi(H) = \begin{cases} 1+\pi(H^{k}) & \text{if } \pi(H^{k})\geq 1-\frac{1}{k}; \\
                              1+\left(\frac{1}{k(1-\pi(H^{k}))}\right)^{1/(k-1)}\left(1-\frac{1}{k}\right) & \text{otherwise.} \end{cases}$$

[**Proof:**]{} For each $n\in \mathbb{N}$, let $G_{n}$ be any $H$-free graph $n$ vertices with $h_{n}(G_{n})=\pi_{n}(H)$. Partition the vertices of $G_{n}$ into $X_{n}=\{v\in V(G_{n}):\{v\}\in E(G)\}$ and $\bar{X_{n}}$ containing everything else. Say that $|X_{n}|=x_{n}n$ and $|\bar{X_{n}}|=(1-x_{n})n$ for some $x_{n}\in [0,1]$. Since $(x_{n})$ is a sequence in $[0,1]$ it has a convergent subsequence. Consider $(x_{n})$ to be the convergent subsequence, and say that $x_{n}\to x\in [0,1]$. With the benefit of hindsight, we know that $x>0$, however, for the upper bound portion of this proof 