How to calculate the negation of an equation

Question

Let a⪯b⪯c⪯da⪯b⪯c⪯d be the variable ordering.
ϕ= a&!b&!c&!d|b&!a&!c&!d|c&d|c&!d|d&!a&!c
X={c,d} is the set of quantified variables. Compute the ROBDD of the existential quantification formula ∃X..¬ϕ using the Exists algorithm, and convert the result to Shannon normal form.

How to calculate ¬ϕ?

Is it using the truth table? do we take the DNF?

Answer 1

Best way to solve this is to first compute the BDD for the given formula Phi. The BDD of its negation is obtained from that BDD by switching the leaf nodes.