Consider the Bayesian Network Structure Below, decide whether the statements are true or false.
b) $G \perp \!\!\! \perp A$ (G is independent of A)
c) $E \perp \!\!\! \perp H | \{D,G\}$ (E and H are conditionally independent given D and G).
d) $E\perp \!\!\! \perp H | \{C,D,F\}$ (E and H are conditionally independent given C,D and F).
b) For these problems I applied the d-separation algorithm as explained here http://web.mit.edu/jmn/www/6.034/d-separation.pdf Using this approach I found that G and A are indeed independent.
c) True (using d-separation).
d) Also true (d-separation).
Could anyone please verify/correct my answers? I feel like at least one of the problems $b,c$ or $d$ should be false.
d) is false. H and E are connected through G in the d-seperation method.