Is this truth table correct?

Question

Is this truth table correct? Sorry for the formatting

Truth table for $p ∧ c$ and $p ∨ c$, with $c$ representing a contradiction:

$$\begin{array}{cc|cc} p & c & p∧c&p∨c \\ \hline T & F & F & T \\ F & F & F & F \end{array} $$

Answer 1

Yes, assuming you are using $c$ to denote a contradiction, then your truth-table is just fine.

Another way you might want to signify a contradiction is by using $\bot$: \bot, and just as an FYI, you can denote a tautology $\top$: \top. These are more universally recognized as contradiction, tautology, respectively. As you can see, some may mistaken $c$ as signifying a variable which can be assigned the truth-values "T" and "F".

Answer 2

\begin{align} &p &c &&p\land c &&p\lor c \\ &T &T &&T &&T \\ &T &F &&F &&T\\ &F &T &&F &&T\\ &F &F &&F &&F \end{align}

just according to the definitions of the truth functions $$\lor:\{T,F\}\rightarrow\{T,F\}$$ and $$\land:\{T,F\}\rightarrow\{T,F\}$$