The statement in the image is a logical proposition:

Prove: $\left( R \land \left( G R \rightarrow W \right) \right) \rightarrow \left( P \land Q \equiv \left( P \rightarrow Q \right) \rightarrow \neg R \right)$

To prove this, let's break it down step by step. Here's a general outline of the approach:

1. Understand the symbols and their meanings:

   • $R, G, W, P, Q$ are propositions.
   • $\rightarrow$ represents implication.
   • $\land$ represents conjunction (AND).
   • $\neg$ represents negation (NOT).
   • $\equiv$ means logical equivalence.

2. Simplify the components:

   • Start by simplifying the left-hand side of the implication $\left( R \land ( G R \rightarrow W ) \right)$.
   • Then proceed to understand the right-hand side $\left( P \land Q \equiv ( P \rightarrow Q ) \rightarrow \neg R \right)$.

3. Prove the equivalence on the right-hand side:

   • Show how $P \land Q \equiv ( P \rightarrow Q )$ leads to $\neg R$.

4. Conclude the proof:

   • Show that the left-hand side implies the right-hand side.

Would you like me to go into more detail for each step, or do you have a specific part of the proof you would like to focus on?