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

- anonymous

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- anonymous

@jim_thompson5910 is this the same as the last ones?

- jim_thompson5910

q: Jose is not winning the race.

- jim_thompson5910

~q is the opposite of q

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## More answers

- jim_thompson5910

So if q says one thing
then ~q (NOT q) says the complete opposite thing q says

- jim_thompson5910

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

- anonymous

so then its p?

- jim_thompson5910

p is the statement Jose is running track

- jim_thompson5910

agreed?

- anonymous

yea

- jim_thompson5910

does that have anything to do with "Jose is winning the race" ?

- anonymous

not really

- jim_thompson5910

so "Jose is winning the race" doesn't involve p at all

- jim_thompson5910

reread what I wrote at the beginning of this thread

- jim_thompson5910

and hopefully something will click

- anonymous

q?

- jim_thompson5910

closer, but still no

- anonymous

~q

- jim_thompson5910

you got it

- jim_thompson5910

look above to see why

- jim_thompson5910

I wrote it out at the top

- anonymous

ohh i didnt even relize it, wow.... thank you so much, i also have 2 more, i have one that i really dont know

- jim_thompson5910

its ok, i was wondering about that lol

- anonymous

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

- jim_thompson5910

First off, is that argument valid?

- jim_thompson5910

oh wait, nvm they're asking a different question

- anonymous

a.) [(p → q) ∧ ~q]
.'.p
b.)[(p → q) → q]
∴ p
c.)[(p → q) ∧ q]
∴ q
d.) [(p → q) ∧ q]
∴ p

- jim_thompson5910

hmm interesting way to put it

- jim_thompson5910

"If Mario studies hard, then he gets good grades." translates to ...???

- anonymous

p?

- jim_thompson5910

p is just "Mario studies hard"

- jim_thompson5910

how do we incorporate the "he gets good grades" part?

- anonymous

p -> q

- jim_thompson5910

good

- jim_thompson5910

"If Mario studies hard, then he gets good grades." translates to p -> q

- jim_thompson5910

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 ???

- anonymous

[(p → q) ∧ ~q] .'. p

- jim_thompson5910

not quite

- jim_thompson5910

~q means he did NOT get good grades, but it clearly says he did

- anonymous

[(p → q) ∧ ~q]
.'. p

- anonymous

[(p->q) ^q] .'. p

- jim_thompson5910

better

- anonymous

so is that it then?

- jim_thompson5910

yes it is

- anonymous

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

- jim_thompson5910

In general
Original = contrapositive
and
inverse = converse

- jim_thompson5910

So it's b)

- jim_thompson5910

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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