supple shell
Hi, I’m working on a homework problem in math about arguments and validity.
I’m supposed to use a truth table to check validity. I know how to set up the premises and conclusion, but I’m not sure how to organize the table and how exactly to check which rows “count” for determining validity.
I missed a lesson unfortunately and want to catch up (I left some rules and 2 question examples if anyone can help :d
Could someone walk me through the steps or show me what my truth table should look like?
radiant epochBOT
carmine pivot
so first, set up your p and q
or whatever variables are in use
then, use p and q to determine the truth values of each premise and the conclusion
then use the validity implication shown in the first picture to check if the argument is valid
if one or more of your premises is just either p or q, then use that column as one of the premises when checking validity
supple shell
If a premise evaluates to false in a truth table row, does that mean the premise isn’t true for that row and I can ignore it when checking validity?
supple shell
if one or more of your premises is just either p or q, then use that column as o...
ohh
carmine pivot
If a premise evaluates to false in a truth table row, does that mean the premise...
yup. vacuous truth still holds here
ideally, you are looking for rows where all premises are true, but the conclusion false
if no such row exists, then your argument is valid
if at least one such row exists, your argument is invalid
wanna try one of them right now? I'll be watching your attempt
supple shell
OHH okay so the argument is only invalid only if there exists a row where all premises are true but the conclusion is false.
carmine pivot
at least one such row, yes
because remember how an implication works
an implication, at least a forward one, is only false if the antecedent is true but the consequent false
the antecedent here is the conjunction of all premises and the consequent is the conclusion
supple shell
an implication, at least a forward one, is only false if the antecedent is true ...
ahh okay and correct me if I’m wrong but when comparing premises to see if the argument would be true we’re just looking to see if they share a common row where they’re both true
carmine pivot
more specifically, please?
supple shell
more specifically, please?
but IF they do share a common truth value in a row and the conclusion is invalid the whole thing is invalid ( sorry this is just ruling i was wondering if this sounds right )
carmine pivot
ok, quick terminology correction
validity only applies to arguments. premises, statements, and conclusions can only be true or false
supple shell
AH i see
carmine pivot
but IF they do share a common truth value in a row and the conclusion is invalid...
the first part is shaky. you said that the premises need only share a common truth value with the conclusion being false to make the argument invalid.
supple shell
validity can only be the whole argument
carmine pivot
this is not correct as stated. if all the premises are false, then they still share a common truth value, but by vacuous truth the argument still holds for that row
but if you meant the stronger condition of requiring all premises be true, then your statement is correct.
supple shell
this is not correct as stated. if all the premises are **false**, then they stil...
yes you're right sorry that wasnt phrased right at all, let me try again. if even a single row in both premises are both true (and for instance lets pretend that the conclusion is true ) then it would be valid?
carmine pivot
if all premises are true in a single row, and the conclusion is also true, the argument holds for that row and that row only
you can only say the argument is valid if the above statement holds for every row
supple shell
OKOK so one row just shows it works there, but for validity it has to work in every row where the premises are true.
But what we are actually keeping an eye for is to see where both premises are true but the conclusion is false WHICH would make the argument invalid because its promising that the consequent should be true when it didnt happen
carmine pivot
yup, basically that
supple shell
DOES that sound right??
omg that feels rewarding finally kind of getting it
thank you
carmine pivot
sure thing
I was actually waiting for that
you can even try a couple if you want. I'll check them
supple shell
you can even try a couple if you want. I'll check them
OKOK so im trying this one
first i found the truth values for both of the premises
p -> q = Tftt
~p = fftt
q = tftf
and i saw that in the last row for both the premises they were true but the conclusion was false
so it would be invalid right?
carmine pivot
could you please make it into a table 😅