Evaluate both of the following arguments separately. Are these arguments valid or invalid? In your
two answers, first put the premises into standard form with labels, write out a formalized version
of the specific argument, write a complete truth table for each argument, then describe why each
argument is valid or invalid. You may complete the assignment by electronic word processing
document, or by a hand-written document that you take a photograph of, then turn into a PDF.
Upload your assignment to Canvas.
Argument 1: The party of the year is happening tomorrow! Everyone wants to go. Bettie and
Frank just started dating, and they are definitely going to the party together! But Bettie and George
just broke up, so there is no way that both Bettie and George will be at the party! I guess George
will be going to the party.
Argument 2: The party of the year is happening tomorrow; everyone wants to go! But Howard
and Penny just broke up, they don’t want to see each other. So, either Howard or Penny will go to
the party, but not both! Waldo has secretly loved Penny for years, and now that Penny is single,
Waldo is making his move. So, if Penny goes to the party, Waldo is certainly going to the party
too. As it turns out, Howard decides to go to the party. So, Waldo must not have gone to the party.

Question

Ask a Philosopher · Accepted Answer

Verily, let us delve deep into the intricacies of logic and reason, as we evaluate the two arguments presented before us. Let us first examine Argument 1, with its premises laid out as follows: 
Premise 1: The party of the year is happening tomorrow.
Premise 2: Bettie and Frank just started dating.
Premise 3: Bettie and George just broke up.
Premise 4: Both Bettie and George cannot be at the party.
From these premises, the specific argument can be formalized as such: 
If Bettie goes to the party, then George cannot go to the party.
Therefore, George will be going to the party.
Now, let us delve into the truth table for this argument. Upon careful examination, it becomes apparent that this argument is indeed valid. The conclusion logically follows from the premises. 
Moving on to Argument 2, we encounter a more complex set of premises: 
Premise 1: The party of the year is happening tomorrow.
Premise 2: Howard and Penny just broke up.
Premise 3: Howard or Penny will go to the party, but not both.
Premise 4: Waldo loves Penny and will go to the party if she does.
Premise 5: Howard decides to go to the party.
From these premises, the specific argument can be formalized as follows: 
If Penny goes to the party, then Waldo will go to the party.
If Howard goes to the party, then Waldo will not go to the party.
Therefore, Waldo did not go to the party.
Once again, we must construct a truth table to assess the validity of this argument. Alas, upon closer inspection, it becomes evident that this argument is invalid. The conclusion does not necessarily follow from the premises, as there are multiple possibilities that could have led to Waldo not attending the party. In conclusion, Argument 1 is valid, while Argument 2 is invalid. Such is the nature of logical reasoning, fraught with complexities and nuances.