Based on the given statements, we can establish a logical chain of relationships using set theory or syllogism:

1. Every red is blue: This means the set of Red ($R$) is a subset of Blue ($B$). So, $R \subset B$.
2. Every blue is green: This means the set of Blue ($B$) is a subset of Green ($G$). So, $B \subset G$.
3. Every green is yellow: This means the set of Green ($G$) is a subset of Yellow ($Y$). So, $G \subset Y$.

Combining these premises, we get a continuous chain of subsets: $R \subset B \subset G \subset Y$

Now, let us evaluate the given conclusions:

• Statement $P$ (Every blue is yellow): Since $B \subset G$ and $G \subset Y$, it logically follows that $B \subset Y$. Thus, statement $P$ is correct.
• Statement $Q$ (Every red is green): Since $R \subset B$ and $B \subset G$, it logically follows that $R \subset G$. Thus, statement $Q$ is correct.
• Statement $R$ (Every red is yellow): Since $R \subset B$, $B \subset G$, and $G \subset Y$, it logically follows that $R \subset Y$. Thus, statement $R$ is correct.

Since all three statements $P$, $Q$, and $R$ are logically deduced from the premises, the correct option is D.