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Mathematics 20 Online
OpenStudy (anonymous):

. Fill in the heading of the following truth table using any of p, q, Use keyboard shortcuts of --> for , <--> for ?, V for V , and ^ for ^ . p q _________ T T F T F T F T T F F T

OpenStudy (anonymous):

i missed some of the symbolic forms. ~, -->, <-->, V , ^

OpenStudy (anonymous):

hi jim

OpenStudy (anonymous):

ok

jimthompson5910 (jim_thompson5910):

p v q is true when either p or q is true

OpenStudy (anonymous):

~(p^q)

OpenStudy (anonymous):

v is Or right?

OpenStudy (anonymous):

that wouldnt be this case though cuz the row 1 column 3 is a F and T T T

jimthompson5910 (jim_thompson5910):

one sec, not done

OpenStudy (anonymous):

ok

jimthompson5910 (jim_thompson5910):

compare the tables of p v q and ~(p v q)

jimthompson5910 (jim_thompson5910):

you'll see that the last columns are the complete opposite

OpenStudy (anonymous):

yup

jimthompson5910 (jim_thompson5910):

so this shows us that the answer for the blank is ~(p v q)

jimthompson5910 (jim_thompson5910):

now, if you want, you can use De Morgan's Law (if your class is onto that topic) and simplify to get ~p ^ ~q

OpenStudy (anonymous):

shouldn't it be ~(p^q) ?

OpenStudy (anonymous):

how ?cuz its f t t t .... thats what they want is the symbolic form for the final column

jimthompson5910 (jim_thompson5910):

oh right, I'm looking at the wrong table, sry one sec more

jimthompson5910 (jim_thompson5910):

ok, yeah it's ~(p ^ q) because the table for p ^ q is p q p ^ q ------------- T T T T F F F T F F F F So the table for ~(p ^ q) is p q ~(p ^ q) ------------- T T F T F T F T T F F T

jimthompson5910 (jim_thompson5910):

lost track of the truth values somehow

OpenStudy (anonymous):

lol

jimthompson5910 (jim_thompson5910):

the truth is out there... anyway, the answer is ~(p ^ q) and you can use De Morgan's Law to expand it out to ~p v ~q

OpenStudy (anonymous):

nah just the basic answer lol thank you :)

jimthompson5910 (jim_thompson5910):

np

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