## Esmy Group Title Use truth tables to test the validity of the argument. p → ~q q → ~p ∴ p ∨ q one year ago one year ago

1. Esmy Group Title

this is valid

2. Esmy Group Title

Case p=T and q=T [(p -> ~q) ^ (q -> ~p)] -> (p V q) [(T -> ~T) ^ (T -> ~T)] -> (T V T) [(T -> F ) ^ (T -> F)] -> T [ F ^ F ] -> T F -> T T

3. Esmy Group Title

All four cases come out T, so the argument is valid. I think lol.

4. A.Avinash_Goutham Group Title

u need to verify that using a truth table?

5. Esmy Group Title

p q ~p ~q p -> ~q q -> ~p p v q T T F F F F T T F F T T T T F T T F T T T F F T T T T F Hmmm... I change my answer its invalid

6. A.Avinash_Goutham Group Title

then u need to make a dumbo table with all the combinations of p and q and verify it or u can use this p->q = (~p) v q

7. Esmy Group Title

"p -> ~q" and "q -> ~p" the last row has T and T so the conclusion is false?

8. A.Avinash_Goutham Group Title

actuall it mean that u shud conside the cases on when both of them are true

9. Esmy Group Title

Oh I totally miss understood the question

10. Esmy Group Title

So how would you do that? :o

11. Esmy Group Title

help can you explain to how you do it :/

12. A.Avinash_Goutham Group Title

consider those case when p → ~q q → ~p are true find them

13. Esmy Group Title

can you explain like in steps :/ I understand in steps.

14. A.Avinash_Goutham Group Title

hmm consider those inputs for which p → ~q is true q → ~p is true

15. Esmy Group Title

umhmm :o

16. A.Avinash_Goutham Group Title

lol sorry....... u shud try and understand

17. A.Avinash_Goutham Group Title

ok fine q → ~p is true for first three columns in the table

18. Esmy Group Title

uhmm :o

19. Esmy Group Title

p q ~p ~q ∼p∨q (∼p∨q)→ ∼q ———————————————————————————————— T T F F T F T F F T F T F T T F T F F F T T T T Like this :D

20. Esmy Group Title

Help D:

21. A.Avinash_Goutham Group Title

u dont need help gal jus think

22. Esmy Group Title

Blagh I am thats why I'm asking if I did right or not

23. Esmy Group Title

Okay I'm guessing i didn't do that one right so ill work on another one.

24. A.Avinash_Goutham Group Title

lol draw truth tables for p → ~q q → ~p and pvq see when p → ~q q → ~p are true pvq is true

25. Esmy Group Title

(~p V q) --> ~q (~T V F) --> ~F (F V F) --> T F --> T T So (~p V q) --> ~q is true.

26. Esmy Group Title

there

27. Esmy Group Title

Blagh W/e I'm right I've done everything... :l

28. Esmy Group Title

q p (q → ~p) → (q ∧ ~p) T T T T F T F T F F F F

29. satellite73 Group Title

the first two statements are identical $p\to \lnot q\iff q\to \lnot p$ one is the contrapositive of the other

30. Esmy Group Title

hmmm is my table okay :/ ?

31. Esmy Group Title

I've done like three so far -_-

32. satellite73 Group Title

let me right it correctly $\begin{array}{|c|c|c|c|c|c} P & Q & \lnot{}P & \lnot{}Q & P\to\lnot{}Q & Q\to\lnot{}P \\ \hline T & T & F & F & F & F \\ T& F & F & T & T & T \\ F & T & T & F & T & T \\ F & F & T & T & T & T \\ \hline \end{array}$

33. satellite73 Group Title

write

34. phi Group Title

the final step is put in the column p v q (this is the first problem) An argument is INVALID if and only if it is logically possible for the conclusion to be false even though every premise is assumed to be true.

35. satellite73 Group Title

if you want to check your truth table, use this nice site here takes a second to get used to 0 and 1 instead of T and F, and a minute to learn the syntax but it is really useful http://www.kwi.dk/projects/php/truthtable/?

36. satellite73 Group Title

but try to think "logically" meaning like a human being instead of using T and F the first statement and the second statement are identical, one is the contrapositive of the other. so you do not need them both, they say the same thing

37. Esmy Group Title

so none of my tables where right :/ ...

38. phi Group Title

this looks ok, The argument is invalid because of the last row p q ~p ~q p -> ~q q -> ~p p v q T T F F F F T T F F T T T T F T T F T T T F F T T T T F Hmmm... I change my answer its invalid

39. satellite73 Group Title

P: it is raining Q: i will go to the store $$P\to \lnot Q$$ if it is raining then i will not go the the store $$Q\to \lnot P$$ if i go to the store, then it is not raining they are identical statements from that, can we conclude that is is raining or i go to the store?

40. satellite73 Group Title

of course not! maybe it is sunny and i stay home anyway!

41. Esmy Group Title

Oh okay :o... I c I c

42. phi Group Title

I don't see the other problems..... with premises and conclusion

43. Esmy Group Title

neither do I

44. phi Group Title

I mean, did you post them?

45. Esmy Group Title

yeah I did ?

46. phi Group Title

Is this one of the problems (~p V q) --> ~q ? with premise ~p v q and conclusion ~q

47. Esmy Group Title

I posted my answer and everything D:?

48. phi Group Title

because it looks invalid p q (~p V q) ~q 0 0 1 1 OK 0 1 1 0 INVALID 1 0 0 1 OK 1 1 1 0 INVALID

49. Esmy Group Title

did you do this one or I did I forgot...

50. phi Group Title

somewhere way up above you typed (~p V q) --> ~q (~T V F) --> ~F (F V F) --> T F --> T T So (~p V q) --> ~q is true. I am not sure what the problem is, I'm guessing the first line. But your conclusion is not correct, because you did not test every case

51. Esmy Group Title

Oh lol thats just one of them lol. I did so many that I got lost ... but that I found out wasn't correct after all the thinking ;l

52. phi Group Title

good, sounds like you have a handle on it.