Question 485670
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


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