Conditional independence in Bayesian network with qualitative influences

Question

I have some troubles solving an exercise from the book Probabilistic Graphical Models (pgm.stanford.edu).

We are given the bayesian network with binary-valued variables.

We do not know the CPDs, but do know how each random variable qualitatively affects its children. The influences, shown in the figure, have the following interpretation:

For each of the following pairs of conditional probability queries, use the information in the network to determine if one is larger than the other, if they are equal, or if they are incomparable. For each pair of queries, indicate all relevant active trails, and their direction of influence.

P(t=1|d=1)         [ ] P(t=1)
P(d=1|t=0)         [ ] P(d=1)
P(h=1|e=1,f=1)     [ ] P(h=1,e=1)
P(c=1|f=0)         [ ] P(c=1)
P(c=1|h=0)         [ ] P(c=1)
P(c=1|h=1,f=0)     [ ] P(c=1|h=0)
P(d=1|h=1,e=0)     [ ] P(d=1|h=1)
P(d=1|e=1,f=0,w=1) [ ] P(d=1|e=1,f=0)
P(t=1|w=1,f=0)     [ ] P(t=1|w=1)

My question is: how are active trails suppose to help me and which are relevant? How do they indicate (in)comparability or equality of these pairs?

(I don't want raw solution. I need to understand how to solve it.)

Answer 1

Active trails are used to find d-seperations, if two nodes are d-seperated, they are irrelevent. D-seperation means no active trails between two node-sets.