hali12
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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hali12
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@jim_thompson5910 is this the same as the last ones?
jim_thompson5910
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q: Jose is not winning the race.
jim_thompson5910
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~q is the opposite of q
jim_thompson5910
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So if q says one thing
then ~q (NOT q) says the complete opposite thing q says
jim_thompson5910
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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
hali12
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so then its p?
jim_thompson5910
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p is the statement Jose is running track
jim_thompson5910
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agreed?
hali12
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yea
jim_thompson5910
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does that have anything to do with "Jose is winning the race" ?
hali12
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not really
jim_thompson5910
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so "Jose is winning the race" doesn't involve p at all
jim_thompson5910
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reread what I wrote at the beginning of this thread
jim_thompson5910
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and hopefully something will click
hali12
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q?
jim_thompson5910
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closer, but still no
hali12
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~q
jim_thompson5910
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you got it
jim_thompson5910
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look above to see why
jim_thompson5910
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I wrote it out at the top
hali12
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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
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its ok, i was wondering about that lol
hali12
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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
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First off, is that argument valid?
jim_thompson5910
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oh wait, nvm they're asking a different question
hali12
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a.) [(p → q) ∧ ~q]
.'.p
b.)[(p → q) → q]
∴ p
c.)[(p → q) ∧ q]
∴ q
d.) [(p → q) ∧ q]
∴ p
jim_thompson5910
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hmm interesting way to put it
jim_thompson5910
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"If Mario studies hard, then he gets good grades." translates to ...???
hali12
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p?
jim_thompson5910
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p is just "Mario studies hard"
jim_thompson5910
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how do we incorporate the "he gets good grades" part?
hali12
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p -> q
jim_thompson5910
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"If Mario studies hard, then he gets good grades." translates to p -> q
jim_thompson5910
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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 ???
hali12
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[(p → q) ∧ ~q] .'. p
jim_thompson5910
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not quite
jim_thompson5910
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~q means he did NOT get good grades, but it clearly says he did
hali12
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[(p → q) ∧ ~q]
.'. p
hali12
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[(p->q) ^q] .'. p
jim_thompson5910
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better
hali12
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so is that it then?
jim_thompson5910
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yes it is
hali12
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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
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In general
Original = contrapositive
and
inverse = converse
jim_thompson5910
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So it's b)
jim_thompson5910
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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