Are the following contradictions? I have the following:
$p\to (q\land p)$
$p\to \neg (q\land p)$
I am asked if they are contradictions, can someone explain what that means exactly. 
I did a truth table for both, and if p is True, then both equations are True, does this imply that they are not contradictions? Or, does contradiction simply mean that only one row in the truth table must differ?
 A: 
I did a truth table for both, and if p is True, then both equations are True, 

Wrong.   An implication holds true only if the consequent is true whenever the antecedent is.   Yet if $p$ is true then the consequents of the two statements cannot both be true.
The two statements have the following equivalences.
$$p\to (q\wedge p) \iff \neg p \vee q
\\[2ex]
p\to \neg (q\wedge p) \iff \neg p \vee \neg q$$
$$\boxed{\begin{array}{c|c|c|c}
p & q & p\wedge q & p\to (p\wedge q) & p\to \neg(p\wedge q) \\ \hline
  &   &           & \neg p\vee q    & \neg p\vee \neg q \\ \hline
T & T & T         & T                & F \\
T & F & F         & F                & T \\
F & T & F         & T                & T \\
F & F & F         & T                & T \\
\end{array}}$$
However, since it is possible for the two statements to both be true for some $p,q$, then these two statements do not contradict each other.
Two statements contradict each other only if their truth evaluations are opposed for all possible values of their variables.
A: No, they are not contradictions because (1) neither statement is a tautology or contradiction in its own right, and (2) the statements' truth values are not diametrically opposed (i.e., they are not opposites). 
