Question

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

Answer 1

@jim_thompson5910 is this the same as the last ones?

Answer 2

q: Jose is not winning the race.

Answer 3

~q is the opposite of q

Answer 4

So if q says one thing

then ~q (NOT q) says the complete opposite thing q says

Answer 5

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

Answer 6

so then its p?

Answer 7

p is the statement Jose is running track

Answer 8

agreed?

Answer 9

yea

Answer 10

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

Answer 11

not really

Answer 12

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

Answer 13

reread what I wrote at the beginning of this thread

Answer 14

and hopefully something will click

Answer 15

q?

Answer 16

closer, but still no

Answer 17

~q

Answer 18

you got it

Answer 19

look above to see why

Answer 20

I wrote it out at the top

Answer 21

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

Answer 22

its ok, i was wondering about that lol

Answer 23

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

Answer 24

First off, is that argument valid?

Answer 25

oh wait, nvm they're asking a different question

Answer 26

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

Answer 27

hmm interesting way to put it

Answer 28

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

Answer 29

p?

Answer 30

p is just "Mario studies hard"

Answer 31

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

Answer 32

p -> q

Answer 33

good

Answer 34

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

Answer 35

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 ???

Answer 36

[(p → q) ∧ ~q] .'. p

Answer 37

not quite

Answer 38

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

Answer 39

[(p → q) ∧ ~q]
.'. p

Answer 40

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

Answer 41

better

Answer 42

so is that it then?

Answer 43

yes it is

Answer 44

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

Answer 45

In general

Original = contrapositive

and

inverse = converse

Answer 46

So it's b)

Answer 47

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