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Convert the following equations into conjunctive normal form.

I tried to solve this question in 2 ways.

once with "Multiplying-out":

and also with "Shannon decomposition":

but each time I got a different answer and I don't know why. Would you please tell me what I did wrong in  Shannon decomposition?

in * TF "Emb. Sys. and Rob." by (1.7k points)

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The correct rule with Shannon decomposition is 

    (x | phi[x<-0]) & (!x | phi[x<-1]) 

and using it you get

     (x <-> (y1 | y2)) 
     <-> ((x | !(y1 | y2)) & (!x | (y1 | y2)) )
     <-> (x | !y1 & !y2) & (!x | y1 | y2) 
     <-> (x | !y1) & (x | !y2) & (!x | y1 | y2) 

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