请教一道关于数理逻辑的问题。

gamecrazyUID: 191024

How many pairwise inequivalent propositional formulas are there us-
ing the propositional variables p1....pn?

Put another way, if the set S = Q1,.....Qn of propositional formu-
las has the property that for every propositional formula P using the
variables p1; : : : ; pn is equivalent to Qj for just one j = 1; : : : ; n, then
how many elements does S have? Let us call such a set S a representative
set of propositional formulas in the variables p1; : : : ; pn; this is not
quite standard terminology.
[Hint: Two formulas Q and P are equivalent just when they have the
same end result for every line of their truth tables.]


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There's a slight grammatical error. It should be worded like this:

"If the set S = (phi(1),...phi(N)) of propositional formulas has the property that every propositional formula Psi using the variables p1,...,pn is equivalent to phi(j) for just one j=1,...,n, then how many elements does S have?"

The rest as far as I can tell is worded fine.


各位怎么看这个问题？

cqlwxUID: 2420288

破海沧澜UID: 2401581

这个问题有点专业...:rolleyes: 回答不上来....:(