In the following proof, which justification is correct for line 4? $\begin{array}{llcc}
\text { (1) $ (x)[(T x \cup D x) \supset F x] $ } & \text {$I(x)(\mathrm{D} x \supset \mathrm{F} x)$ }& \text { Premise/Conclusion } \
\text { (2) $ \mathrm{Da} $ } && \text { Assumption}\
\text { (3) $ (\mathrm{Ta} \vee \mathrm{Da}) \supset \mathrm{Fa} $} && \text { $ 1 \mathrm{UI} $ }\
\text {(4) $ \mathrm{Ta} \cup \mathrm{Da} $ } &\

\end{array}$

Question

In the following proof, which justification is correct for line 4? $\begin{array}{llcc}
  \text { (1) \( (x)[(T x \cup D x) \supset F x] $ } & \text {$I(x)(\mathrm{D} x \supset \mathrm{F} x)$  }& \text { Premise/Conclusion  }  \
 \text { (2) $ \mathrm{Da} $ } && \text {  Assumption}\
 \text {  (3) $ (\mathrm{Ta} \vee \mathrm{Da}) \supset \mathrm{Fa} $} && \text {  $ 1 \mathrm{UI} $ }\
 \text {(4) $ \mathrm{Ta} \cup \mathrm{Da} $  } &\

\end{array}\)

Quizplus · Accepted Answer

The correct justification for line 4 is "2 Add" because it directly applies the Addition rule to statement 2, indicating that if $Da$ is true, then $Ta \vee Da$ (or $Ta \cup Da$ using the symbol in the question) is also true.

In the Following Proof, Which Justification Is Correct for Line