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Alright, have another one which the solutions manual is vague on.
I have to reduce \$f =(x1+x3+x4)(x1+x2'+x3)(x1+x2'+x3'+x4)\$. Right in the first step, though, the solution does something I don't understand.
They go to \$(x1+x3+x4)(x1+x2'+x3)(x1+x2'+x3+x4)(x1+x2'+x3'+x4)\$. Where did that 4th term come from? I thought we could add a sum if it was the same as one of the current terms? How are they allowed to change the x3?
I assume your question is about boolean algrbra and you are using \$'\$ to represent a not operation \$+\$ to indicate a "inclusive or" operation and no symbol at all to denote a "and" operation.
I think they are replacing
\$(x1+x2'+x3)\$
With
\$(x1+x2'+x3)(x1+x2'+x3+x4)\$
This will not change the result because whenever \$(x1+x2'+x3)\$ is 1
\$(x1+x2'+x3+x4)\$ will also be 1.
