Let p and q represent the statements: p: Jose is running track. q: Jose is not winning the race. Express the following statement symbolically: Jose is winning the race..... a) p.. b) q.. c)~q.. d) ~p

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Let p and q represent the statements: p: Jose is running track. q: Jose is not winning the race. Express the following statement symbolically: Jose is winning the race..... a) p.. b) q.. c)~q.. d) ~p

Mathematics
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@jim_thompson5910 is this the same as the last ones?
q: Jose is not winning the race.
~q is the opposite of q

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Other answers:

So if q says one thing then ~q (NOT q) says the complete opposite thing q says
so ~q is like saying Jose is NOT not winning the race ...a bit confusing, but the two "not"s cancel giving us ~q: Jose is winning the race
so then its p?
p is the statement Jose is running track
agreed?
yea
does that have anything to do with "Jose is winning the race" ?
not really
so "Jose is winning the race" doesn't involve p at all
reread what I wrote at the beginning of this thread
and hopefully something will click
q?
closer, but still no
~q
you got it
look above to see why
I wrote it out at the top
ohh i didnt even relize it, wow.... thank you so much, i also have 2 more, i have one that i really dont know
its ok, i was wondering about that lol
Look at the argument below. Which of the following symbolic statements shows the set-up used to find the validity of the argument? If Mario studies hard, then he gets good grades. Mario got good grades. Therefore, Mario studied hard. p: Mario studies hard. q: Mario gets good grades
First off, is that argument valid?
oh wait, nvm they're asking a different question
a.) [(p → q) ∧ ~q] .'.p b.)[(p → q) → q] ∴ p c.)[(p → q) ∧ q] ∴ q d.) [(p → q) ∧ q] ∴ p
hmm interesting way to put it
"If Mario studies hard, then he gets good grades." translates to ...???
p?
p is just "Mario studies hard"
how do we incorporate the "he gets good grades" part?
p -> q
good
"If Mario studies hard, then he gets good grades." translates to p -> q
now tack on the statement "Mario got good grades" So what does "If Mario studies hard, then he gets good grades. Mario got good grades. " translate to ???
[(p → q) ∧ ~q] .'. p
not quite
~q means he did NOT get good grades, but it clearly says he did
[(p → q) ∧ ~q] .'. p
[(p->q) ^q] .'. p
better
so is that it then?
yes it is
oh ok, thanks, and this will be the last one i promise,: Which of the following is the equivalent of the inverse statement? a.) the negation of the statement.. b.) the converse of the statement.... c.)the contrapositive of the statement... d.)the conditional statement
In general Original = contrapositive and inverse = converse
So it's b)
the inverse of p -> q is ~p -> ~q -------------- that's equivalent to ~~q -> ~~p which is the same as q -> p but this is the converse So this shows that the inverse and the converse represent the same thing

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