Page 2-39, Question 1

[Blueballoon5%]

Hi! For this question, the answer explanation in the lesson book (on the next page) seems to put the happiness of individuals and their friends/family as one when translating the sentences into diagrams. When I read the question, I made the two separate (below)

Sentence 1: If people have serious financial problems, they cannot be happy (or "SF -H")
Sentence 2: If they cannot be happy, then their friends/family cannot be happy (or "-H -FFH")
sentence 3: If they + their friends/family are happy, then their financial problems are solved (or "H + FFH -SF")

The answer key combined H (person's happiness) and FFH (friends/family's happiness) into just H (happiness). When should we combine the individual's happiness and their friends/family's happiness, and when should we not?

Thanks!!!

[AthenaDalton]

Good question!

I actually don't read the diagrams as conflating "people's happiness" with "friends' and families' happiness." The very short answer to your question is, when there are different terms like this in a conditional reasoning problem, don't conflate them.

Secondly, you can actually solve this problem with just the contrapositive of the first sentence:

Sentence 1: People with serious financial problems . . . cannot be happy.

Diagram Sentence 1: SFP -H

Contrapositive Sentence 1: H -SFP

Correct Answer Choice E: If people are happy, they do not have serious financial problems.

That being said, here's how the rest of the sentences can be diagrammed:

Sentence 1 says "People with serious financial problems cannot be happy."

SFP (Serious Financial Problems) -H (not happy)

Sentence 3 says "Only if their financial problems are solved can they and those around them be happy.

-SFP (No Serious Financial Problems) H (happy)

This diagram refers to the happiness of both (1) the individual and (2) their friends. You could think of it as creating two diagrams. It's not necessary to sketch them out to work this problem, but here's what that would look like:

-SFP (No Serious Financial Problems) Hfriends
-SFP (No Serious Financial Problems) Hindividual

As I mentioned earlier, all of these gymnastics are unnecessary to solve this one, since answer choice (E) is the contrapositive of the first sentence. I hope this clears things up for future reference, though!

Good luck studying!