= Solution
The conditional open probability in part (b) is increasing in the states of all other edges, because adding edges can only connect the two endpoints. A common-uniform update therefore preserves the coordinatewise order. Start two copies from all closed and use the same updates, with the second copy additionally conditioned through an increasing event $B$ by the corresponding monotone censored heat-bath chain. The monotone grand coupling and convergence to stationarity show that conditioning on $B$ stochastically increases the configuration. Hence for increasing $A$,
$$
\phi_{p,2}(A\mid B)\geq\phi_{p,2}(A),
$$
which is the <Harris-FKG inequality> $\phi(A\cap B)\geq\phi(A)\phi(B)$. Applying this to the complement of a decreasing event $B'$ gives
$$
\phi(A\cap B')\leq\phi(A)\phi(B').
$$
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