# Thread: Simple truth table, check if correct

1. ## Simple truth table, check if correct

Im having some trouble with a Simple truth table

the question is consider the following truth statement

~(PV~Q)Λ~Q ** Notion ~ = not , V = or , Λ = and

Questions
1. Express the above logic statement as a logic gates system.
2. write out the truth table fot the system

heres my take on numer two

P, Q, ~Q, PV~Q, ~(PV~Q)
0, 0, 1, 1, 0
0, 1, 0, 0, 1
1, 0, 1, 1, 0
1, 1, 0, 1, 0

can anyone confirm if this is correct?

** edit of the layout came out not as i intended this doesn't seem to recognize more than one space after you submit, i have used a comma to show a different coloum

2. ## Re: Simple truth table, check if correct

Code:
P   Q   ~Q   P V ~Q   ~(P V ~Q)
0   0    1     1          0
0   1    0     0          1
1   0    1     1          0
1   1    0     1          0
This is correct, but it is a truth table for ~(P V ~Q), not ~(P V ~Q) Λ ~Q.

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3. ## Re: Simple truth table, check if correct

Oh right, thanks for that , i seem to have it a bit confused then, what would the headings for ~(P V ~Q) Λ ~Q truth table be then ?

4. ## Re: Simple truth table, check if correct

Originally Posted by ronanbrowne88
what would the headings for ~(P V ~Q) Λ ~Q truth table be then ?
By "headings", do you mean the table's first line? It should be "P Q (~(P V ~Q) Λ ~Q)", i.e., the table should have three columns. You could also add columns for intermediate subformulas ~Q, P V ~Q and ~(P V ~Q), as you did.

5. ## Re: Simple truth table, check if correct

Hello, ronanbrowne88!

Consider the following truth statement: . $\sim(P\,\vee\,\sim\!Q) \wedge \sim\!Q$

1. Express the logic statement as a logic gates system.

$\begin{array}{ccccccc}1. & \sim(P \,\vee\sim\!Q) \wedge \sim\!Q && 1. & \text{Given} \\ 2. & (\sim\!P\wedge Q)\, \wedge \sim\! Q && 2. & \text{DeMorgan} \\ 3. & \sim\!P \wedge (Q\,\wedge\sim\!Q) && 3. &\text{Assoc.} \\ 4. & \sim\!P\,\wedge f && 4. & A\,\wedge \sim\!A \,=\,f \\ 5. & f && 5. & A\wedge f \,=\,f \end{array}$

2. Write the truth table for the system.

. . $\begin{array}{|c|c||c|c|c|c|c|c|} P & Q & \sim & (P & \vee & \sim\!Q) & \wedge & \sim\!Q \\ \hline T&T & F&T&T&F&{\color{red}F}&F \\ T&F&F&T&T&T&{\color{red}F}&T \\ F&T &T&F&F&F&{\color{red}F}&F \\ F&F & F&F&T&T&{\color{red}F}&T \\ \hline &&3 & 1 & 2 & 1 & 4 & 1 \end{array}$