Disjunction with Tautology/Proof 2

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$p \lor \top \dashv \vdash \top$


We apply the Method of Truth Tables to the proposition.

As can be seen by inspection, in each case, the truth values in the appropriate columns match for all boolean interpretations.

$\begin{array}{|c|c||ccc|} \hline p & \top & p & \lor & \top \\ \hline F & T & F & T & T \\ T & T & T & T & T \\ \hline \end{array}$