\begin{problem}{Declaration of Conditional Independence} 
Which of the following statements is true based on the graph below? Select all that apply.

\begin{center}
    \includegraphics[height=0.5\textwidth]{figures/d-separation.png} 
 \end{center}
 
  
\begin{question}[5]
Which of the following statements are true based on the graph below? Select all that apply.

\qquad\solution{\emptysquare}{\ThreeAA} \quad Given C and H and K, A and F are conditionally independent. \quad 

\qquad\solution{\emptysquare}{\ThreeAB} \quad Given D and I and J, E and F are conditionally independent. \quad 

\qquad\solution{\emptysquare}{\ThreeAC} \quad  Given B and I and K, E and F are conditionally independent. \quad 

\qquad\solution{\emptysquare}{\ThreeAD} \quad Given I, A and K are conditionally independent. \quad 

\qquad\solution{\emptysquare}{\ThreeAE} \quad None of the above.
 \quad 

\end{question}

\begin{question}[5]
Given which of the following node(s) would make A and B NOT conditionally independent? Select all that apply.

\qquad\solution{\emptysquare}{\ThreeBA} \quad H \quad 

\qquad\solution{\emptysquare}{\ThreeBB} \quad K \quad 

\qquad\solution{\emptysquare}{\ThreeBC} \quad K and J \quad 

\qquad\solution{\emptysquare}{\ThreeBD} \quad C and D \quad 

\qquad\solution{\emptysquare}{\ThreeBE} \quad None of the above. A and B are not conditionally independent in the original graph.
 \quad 

\end{question}

\end{problem}
