## sandii2006 3 years ago Write the argument below in symbols to determine whether it is valid or invalid. State a reason for your conclusion. Specify the p and q you used. Submit your full detailed solution If the koi are swimming in the pond, then the birds are chirping. The birds are not chirping. The koi are not swimming in the pond.

1. hahd

birds are dependent on koi swimming

2. hahd

if koi dont swim then birds dont chirp

3. 101Ryan101

If the Packers are playing, koi might be swimming.

4. Dangolbery

5. sandii2006

come on guys i'm trying to LEARN THIS please.... no joking around.. I would appreciate it..

6. jim_thompson5910

p: the koi are swimming in the pond q: the birds are chirping So the argument translates to p --> q ~q .: ~p So this is a valid argument since it uses the Modus Tollens form

7. snaef999

if k = s then b = c b != c thus k!=s

8. abtrehearn

$p \rightarrow q$not p therefore, not q. The argument is valid [contrapositive]

9. sandii2006

how come you both got DIFFERENT answers?

10. jim_thompson5910

abtrehearn is using not p instead he should be using not q

11. hahd

p --> q ~q .: ~p

12. jim_thompson5910

but the law of the contrapositive is another way to say modus tollens

13. sandii2006

ok which is the "correct" way to say it jim?

14. jim_thompson5910

not sure which one your book uses

15. sandii2006

i believe it the modus

16. abtrehearn

My mistake.

17. jim_thompson5910

have you seen that term before?

18. hahd

jim is right

19. jim_thompson5910

well you have the law of contrapositive correct (since that's just another way of saying modus tollens)

20. sandii2006

yes i have seen that term before jim

21. jim_thompson5910

22. abtrehearn

Got the p and q backwards.

23. sandii2006

ok thank you. for clarifying it jim :)

24. jim_thompson5910

np