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Consider the propositional formula $((P \land Q) \vee (P \land Q))$. Suppose I were to make a truth table for that formula. I would first make two columns of four rows, representing the possible assignments of $P$ and $Q$ to true and false. Then, I make a column for $(P \land Q)$. Now, here is where I am confused. Do I make a duplicate column for $(P \land Q)$, and then make a column for $((P \land Q) \vee (P \land Q))$, or can I just go straight to $((P \land Q) \vee (P \land Q))$? In other words, what I am really asking is, does one have to duplicate columns for duplicate occurrences of formulas to make a correct truth table?

user107952
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    Matter of taste, not mathematics. As far as I know people don't tend to duplicate columns like that. The only situation in which I would duplicate a column is if it would make it easier for me to read it for the computation of another column. – Snaw Feb 01 '22 at 00:38
  • When constructing truth tables you don't create a new column for each occurrence of the propositional component in a sentence, so I don't see why would you do that for the identical compound components of the given sentence. – anfauglit Feb 01 '22 at 15:11

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