Proving De Morgan laws inductively?

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How can I prove <by induction> the following De Morgan laws are valid for all n >= 2

- ( P(d1) ^ ... ^ P(dn) ) = ( - P(d1) ) v ... v ( - P(dn) )

knowing that -(p^q)=(-p)v(-q) and -((p)v(q))=(-p)^(-q) ?

I can use the inductive proof method on algebra/math theorems that have to do with variables, numbers, series, sums, etc. but I don't know what to do with propositions. Help, anyone?

I know how to prove the De Morgan laws when it comes to sets, I can also do it by deduction, but I'm just curious as to how you'd go about doing this inductively.
 
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Hint: Treat the propositions as formulas in Boolean algebra and use the fact that the operators ^ and v are (individually) associative.
 

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