SOLUTION: please please help me, i have posted this problem several times and no one will respond. if the argument is valid, name which of the four valid forms of argument is represented. i

Click here to see ALL problems on Conjunction

Question 485670: please please help me, i have posted this problem several times and no one will respond.
if the argument is valid, name which of the four valid forms of argument is represented. if it is not valid, name the fallacy that is represented.
if i sing in the shower, then i will not be overheard while singing.
i was overheard while singing
therefore i did not sing in the shower.

Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The argument is valid because the contrapositive of a conditional proposition always has the same truth value as the original proposition:

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if i sing in the shower, then i will not be overheard while singing.
i was overheard while singing
therefore i did not sing in the shower.

this looks like it is valid by the law of contra-position.

the law of contra-position states:

if p then q
not q
therefore not p

let p = i sing in the shower
let q = i will not be overheard while singing.

the statement:
if i sing in the shower then i will not be overheads while singing
translates to:
p -> q

i was overhead while singing translates to:
~q

therefore i did not sing in the shower translates to:
~p

the whole argument of:
if i sing in the shower, then i will not be overheard while singing.
i was overheard while singing
therefore i did not sing in the shower.

translates to:
p -> q
~q
therefore ~p

This is valid by the law of contra-position.

here's some additional information that might be helpful.

v means or
^ means and
~ means not
-> means implies
<-> means is equivalent to

STATEMENT LAWS AND FALLACIES