Question

Can someone help me make a Truth Table for this problem please.. ~p ^ (~r ^ q)

Answer 1

i ored it ...

Answer 2

set up r and q

r -r q -r^q
t f t f
f t t t
f f f
t f f

may be better

Answer 3

p -p -p -r^q -p^(-r^q)
t f f f f
f t f t f
f f f
f f f
t f f
t t t
t f f
t f f

i cant recall if "f.f = t" tho

Answer 4

i have to show the whole process.. for the truth table..
my professor gave me this to start with
p q r ~p ~r ~r ^ q ~p ^ (~r ^ q)
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
now i just have to finish the rest.

Answer 5

You understand the general method of constructing a truth table?

\[\begin{array}{|ccc|c|c|c|c|c} p&q&r&\lnot p & \lnot r & \lnot r\wedge q & \lnot p \wedge(\lnot r \wedge q) \\ \hline T & T& T \\T & T & F \\ T&F & T \\ T & F & F \\ F & T& T \\ F & T & F \\ F & F & T \\ F & F & F\end{array}\]

Answer 6

negate P negate r

Answer 7

yes the ~ is for not... so it would be Not P

Answer 8

Right, so now you just fill up the \(\lnot p\) column with the OPPOSITE of whatever p is for that row.

Answer 9

id do -r^q first, but i think they are associative to begin with

Answer 10

For example I'll do the first 5 in that column:
\[\begin{array}{|ccc|c|c|c|c|c} p&q&r&\lnot p & \lnot r & \lnot r\wedge q & \lnot p \wedge(\lnot r \wedge q) \\ \hline T & T& T & F\\T & T & F & F\\ T&F & T & F \\ T & F & F & F \\ F & T& T & T\\ F & T & F \\ F & F & T \\ F & F & F\end{array}\]

Answer 11

i get discrete math this term :) gonna be doing these in chapter 1

Answer 12

Yep. I did a few of them last semester ;)

Answer 13

So its the opposite for ~r too right?

Answer 14

\(\lnot r \) is the opposite of r yes.

Answer 15

Ok i got ~r done how

Answer 16

how do i do the next row?

Answer 17

Oh drat

Answer 18

It's AND, not or.

Answer 19

so the if either one have a T then its T?

Answer 20

\(\lnot r\) must be T AND q must be T for \(\lnot r \wedge q\) to be T

Answer 21

No, I got the operator wrong. \(\wedge\) is AND. I said OR originally. They must BOTH be True for this column to be True.

Answer 22

ok

Answer 23

practicing your tables Satellite? ;)

Answer 24

so it should be F F F F T T F F

Answer 25

\[\begin{array}{|ccc|c|c|c|c|c} p&q&r&\lnot p & \lnot r & \lnot r\wedge q & \lnot p \wedge(\lnot r \wedge q) \\ \hline T & T& T & F& F & F
\\T & T & F & F& T & T
\\ T&F & T & F & F & F
\\ T & F & F & F &T & F
\\ F & T& T & T & F & F
\\ F & T & F &T & T & T
\\ F & F & T &T & F & F
\\ F & F & F&T & T & F
\end{array}\]

Answer 26

Is that what you got?

Answer 27

yup thats what i got

Answer 28

trying to leap over 3 columns gets my eyes lost :)

Answer 29

lol mine too.
so how do i do the final column?

Answer 30

Ok so now the last column will be True if and only if the \(\lnot p\) is True and the \(\lnot r \wedge q\) column is True.

Answer 31

Because it's \(\lnot p\) AND (\(\lnot r\) AND q)

Answer 32

so it should be f f f f f t f f

Answer 33

I honestly don't know why they use \(\wedge\) and \(\vee\) since it's not any harder to write AND or OR, and it's harder to mix them up.

Answer 34

yea i agree with you there polnak

Answer 35

dont be afraid to re order to columns to make life easier:

\begin{array}{|ccc|c|c|c|c|c} p&r&q&\lnot r & \lnot r\wedge q & \lnot p & \lnot p \wedge(\lnot r \wedge q) \\
\end{array}
perhaps

Answer 36

mine is different

Answer 37

That's because I screwed it up

Answer 38

lol

Answer 39

\[\begin{array}{|ccc|c|c|c|c|c} p&q&r&\lnot p & \lnot r & \lnot r\wedge q & \lnot p \wedge(\lnot r \wedge q) \\ \hline T & T& T & F& F & F & F
\\T & T & F & F& T & T & F
\\ T&F & T & F & F & F & F
\\ T & F & F & F &T & F & F
\\ F & T& T & T & F & F & F
\\ F & T & F &T & T & T& T
\\ F & F & T &T & F & F & F
\\ F & F & F&T & T & F & F
\end{array}\]

Answer 40

Thats what i have :) :)

Answer 41

p r q
----------
-F ^ -F ^ T should be the only "True" you get, regardless of the rest of it :)

Answer 42

Thank you Polnak:) for helping me with this .. i'm sure i will be having MORE of these types of problems lol

Answer 43

just keep your \(\wedge\) = AND, \(\vee\) = OR straight, and you'll be fine.

Answer 44

ok thank you