Determine which, if any, of the three statements are equivalent. Give a reason for conclusion.
I) If the cat does not have claws, then the cat cannot scratch the furniture.
II) If the cat can scratch the furniture, then the cat has claws.
III) If the cat has claws, then the cat can scratch the furniture.

Question

Determine which, if any, of the three statements are equivalent. Give a reason for conclusion. 
I) If the cat does not have claws, then the cat cannot scratch the furniture.
II) If the cat can scratch the furniture, then the cat has claws.
III) If the cat has claws, then the cat can scratch the furniture.

anonymous · Answer

one and three

if p then q
if ~p then ~q

anonymous · Answer

sorry thats not right. those would be inverses, but not the same. its 1 and 2 or none of them

anonymous · Answer

1 and 2

anonymous · Answer

y?

anonymous · Answer

dude, im sorry i am just confusing you. let me try this again.

1 = if ~p then ~q
2 = if p then q
3 = if q then p

anonymous · Answer

i am not a dude by the way i am a 24 year old chick lol :)

anonymous · Answer

i think its none
because 1 and 2 are inverses and the only way 2 and 3 would be the same is if it was a biconditional like this p [tribar] q

anonymous · Answer

and sorry for calling you dude. it has been a year since taking logic. but i am pretty sure 2 and 3 are NOT the same and 1 is NOT the same as either

anonymous · Answer

so you think its none right?

anonymous · Answer

i think so. how many times has it been none? i assume you are working out a problem set

anonymous · Answer

it hasnt been i think you are right... ill just go with that thanks!

anonymous · Answer

def ask your teacher if its right and why

anonymous · Answer

ok will do thanks!