How do you imply $Q\to (P\wedge Q)$ from $P$? Taking a logic course and confused by this question. How do you logically introduce the $Q$ into the proof?
 A: Not sure how you need to show this, but here are some options:
Formal proof
$\def\fitch#1#2{\begin{array}{|l}#1 \\ \hline #2\end{array}}$ 
$\fitch{
1. P \quad \quad \qquad Given}{
\fitch{
2. Q \quad \quad \qquad Assumption}{
3. P \land Q \qquad \quad \land \ Intro \ 1,2\\
}\\
4. Q \to (P \land Q) \quad \to \ Intro \ 2-3\\ 
}$
Truth-Table
\begin{array}{cc|cc}
P&Q&Q&\to&(P \land Q)\\
\hline
T&T&T&T&T\\
T&F&F&T&F\\
F&T&T&F&F\\
F&F&F&T&F\\
\end{array}
So, we see that given that $P$ is true (which means we only have to look at the first two rows), the statement $Q \to (P \land Q)$ is true as well
Informal Proof
If you assume that $Q$ is true, then given that you already have that $P$ is True, $P \land Q$ will be true. So, we have that if $Q$ is true, then $P \land Q$ is true as well. Therefore, we have $Q \to (P \land Q)$
A: I'm not sure if this is what you're asking but given $P$ I'm going to show $Q\implies P\land Q$. To do that, one has to show that if $Q$, then $P\land Q$. Hence, assume $Q$. By hypothesis we have $P$. So we have $P$ and $Q$, i.e. $P\land Q$.
