Conjunction with Tautology/Proof by Truth Table

From ProofWiki
Jump to navigation Jump to search

Theorem

$p \land \top \dashv \vdash p$


Proof

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.

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

$\blacksquare$