## hali12 3 years ago 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

1. hali12

@jim_thompson5910 is this the same as the last ones?

2. jim_thompson5910

q: Jose is not winning the race.

3. jim_thompson5910

~q is the opposite of q

4. jim_thompson5910

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

5. 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

6. hali12

so then its p?

7. jim_thompson5910

p is the statement Jose is running track

8. jim_thompson5910

agreed?

9. hali12

yea

10. jim_thompson5910

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

11. hali12

not really

12. jim_thompson5910

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

13. jim_thompson5910

14. jim_thompson5910

and hopefully something will click

15. hali12

q?

16. jim_thompson5910

closer, but still no

17. hali12

~q

18. jim_thompson5910

you got it

19. jim_thompson5910

look above to see why

20. jim_thompson5910

I wrote it out at the top

21. hali12

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

22. jim_thompson5910

its ok, i was wondering about that lol

23. hali12

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

24. jim_thompson5910

First off, is that argument valid?

25. jim_thompson5910

oh wait, nvm they're asking a different question

26. hali12

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

27. jim_thompson5910

hmm interesting way to put it

28. jim_thompson5910

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

29. hali12

p?

30. jim_thompson5910

p is just "Mario studies hard"

31. jim_thompson5910

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

32. hali12

p -> q

33. jim_thompson5910

good

34. jim_thompson5910

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

35. 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 ???

36. hali12

[(p → q) ∧ ~q] .'. p

37. jim_thompson5910

not quite

38. jim_thompson5910

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

39. hali12

[(p → q) ∧ ~q] .'. p

40. hali12

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

41. jim_thompson5910

better

42. hali12

so is that it then?

43. jim_thompson5910

yes it is

44. hali12

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

45. jim_thompson5910

In general Original = contrapositive and inverse = converse

46. jim_thompson5910

So it's b)

47. 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