Your friend stops by your house and tells you the following

Your friend stops by your house and tells you the following:

“If I get a puppy this summer, then my sister will not come to my pool party. Now, my sister will come to my pool party or my mother will be really upset. I ultimately decided not to get a puppy this summer. So now I know my mother won’t be upset!”

Write your friend’s argument in symbolic form using three component (i.e. single) statements p, q and r. Write these component statements explicitly.

Analyze the argument: is it valid or not? Justify your answer.

Solution

p: getting a puppy

q: sister coming to party

r : mother being upset

so

If I get a puppy this summer, then my sister will not come to my pool party   p --> ~q

my sister will come to my pool party or my mother will be really upset      q ^ r

I ultimately decided not to get a puppy this summer. So now I know my mother won’t be upset!   ~p --> ~r