what would be the truth table for ~(p ∨ q) ∧ ~p?

Question

anonymous · Answer

lets see if i can write a truth table here

anonymous · Answer

what the heck is a truth table? lol

happykiddo · Answer

the explanation the class lesson gives is pretty shoddy
so help very much needed :D

anonymous · Answer

ok lets start step by step

anonymous · Answer

$$\begin{array}{|c|c}
   P
 & Q \
\hline
T& T \
T & F \
F & T \
F& F\
\hline
\end{array}
$$
here is our starting piont, it gives all possible combinations of true and false for the two statemenst p and q

anonymous · Answer

so far so good?

happykiddo · Answer

yep i got that far

anonymous · Answer

now we have a ~p there so lets add that 
$$
\begin{array}{|c|c|c}
   P
 & Q
 & \lnot{}P \
\hline
T & T & F \
T & f & T\
F & T & F \
F & F & T \
\hline
\end{array}$$
we get that by changes all the T to F under P and vice versa
with me so far?

happykiddo · Answer

yep

anonymous · Answer

now we also see a $P\lor Q$ so lets add that 
for that one, all is true unless both P and Q are false

anonymous · Answer

$$\begin{array}{|c|c|c|c}
   P
 & Q
 & \lnot{}P
 & P\lor{}Q \
\hline
T & T & F & T \
T & F & T & T \
F & T & F & F \
F & F & T & T \
\hline
\end{array}$$

happykiddo · Answer

wait a second i thought ~P= F
                                          F
                                          T
                                           T

anonymous · Answer

yes are right. i was so excited to format the table that i made a mistake
good eye

anonymous · Answer

$$\begin{array}{|c|c|c|c}
   P
 & Q
 & \lnot{}P
 & P\lor{}Q \
\hline
T & T & F & T \
T & F & F & T \
F & T & T & F \
F & F & T & T \
\hline
\end{array}$$

anonymous · Answer

that's better

anonymous · Answer

next line. we need $\lnot(P\lor Q)$ so we change all the T to F and vice versa under the line $P\lor Q$

anonymous · Answer

don't worry, only one more to go

anonymous · Answer

$$\begin{array}{|c|c|c|c|c}
   P
 & Q
 & \lnot{}P
 & P\lor{}Q
 & \lnot{}(P\lor{}Q) \
\hline
T & T & F & T & F \
T & F & F & T & F \
F & T & T & F & T \
F & F & T & T & F \
\hline
\end{array}$$

happykiddo · Answer

I thought  PvQ was....T
                               T
                               T
                               F

anonymous · Answer

let me know if  you have any questions thus far
one more and we are done

anonymous · Answer

$$\begin{array}{|c|c|c|c|c}
   P
 & Q
 & \lnot{}P
 & P\lor{}Q
 & \lnot{}(P\lor{}Q) \
\hline
T & T & F & T & F \
T & F & F & T & F \
F & T & T & T & F \
F & F & T & F & T \
\hline
\end{array}$$

anonymous · Answer

well you caught me again. i wasn't thinking, so i guess you know more than you think on this subject

anonymous · Answer

and more than me at this late hour. but now we are good to go right?  because last line is all we need, namely $\lnot(p\lor q)\land \lnot p$

happykiddo · Answer

Well i kinda only need help with the last one the  ~(p ∨ q) ∧ ~p  :)

anonymous · Answer

ok well that is it. we only look at the lines $\lnot(p\lor q)$ and the line $\lnot p$ and

anonymous · Answer

and the $\land$ between them means you only get T if both are T

happykiddo · Answer

but its V

anonymous · Answer

$$\begin{array}{|c|c|c|c|c|c}
   P
 & Q
 & \lnot{}P
 & P\lor{}Q
 & \lnot{}(P\lor{}Q)
 & \lnot{}(P\lor{}Q)\land{}\lnot{}P \
\hline
T & T & F & T & F & F \
T & F & F & T & F & F \
F & T & T & T & F & F \
F & F & T & F & T & T \
\hline
\end{array}$$

happykiddo · Answer

oh nevermind gotcha

anonymous · Answer

if you ever want to generate a nice truth table via the web, and don't mind the fact that they use zeros and ones instead of t and f and write them backwards (zeros first, ones second) try here http://www.kwi.dk/projects/php/truthtable/?

happykiddo · Answer

oh thanks a bunch your a real hombre :D