We can interpret the truth table below to be a demonstration that (q & p) and (p & q) are related to each other in what way(s)? $$\begin{array} { | c | c | c | c | c | }
\hline p & q & ( p \& q ) & ( q \& p ) & ( p \& q ) = ( q \& p ) ) \
\hline T & T & T & T & T \
\hline T & F & F & F & T \
\hline F & T & F & F & T \
\hline F & F & F & F & T \
\hline
\end{array}$$
A) They imply each other.
B) The second does not imply the first.
C) The first does not imply the second.
D) They are both tautologies.
E) They are both inconsistent.

Question

We can interpret the truth table below to be a demonstration that (q & p) and (p & q) are related to each other in what way(s)? $$\begin{array} { | c | c | c | c | c | } 
\hline p & q & ( p \& q ) & ( q \& p ) & ( p \& q ) = ( q \& p ) ) \
\hline T & T & T & T & T \
\hline T & F & F & F & T \
\hline F & T & F & F & T \
\hline F & F & F & F & T \
\hline
\end{array}$$
A) They imply each other.
B) The second does not imply the first.
C) The first does not imply the second.
D) They are both tautologies.
E) They are both inconsistent.

Quizplus · Accepted Answer

The truth table shows that for all combinations of truth values of p and q, (p & q) and (q & p) have the same truth value, which means they imply each other.

We Can Interpret the Truth Table Below to Be a Demonstration