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The number of propositional variables is always at most one more than the number of connectives for every formula φ ∈ PROP.

where PROP is the set which represents all valid formula in propositional logic

I tried doing this proof in various ways, but I could not do it by structural induction.

Can someone explain how structural induction works and also how to prove the above claim using it.

  • A better idea is to read about structural induction and prove it for yourself. Check this out. https://www.cs.umd.edu/class/summer2016/cmsc250/files/slides/structuralInduction.pdf – John Douma Nov 02 '18 at 04:40

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