- Mon Dec 04, 2023 2:12 pm
#104287
Hi Eric,
To be clear, when you diagram a contrapositive, you reverse the terms and negate the terms. To negate a term, if the term is originally positive, then you make it negative (by adding a slash to it in your diagram). However, if a term is originally negative, you negate it by making it positive (by removing the slash in your diagram).
For example, the first sentence of the stimulus is basically saying "if people have serious financial problems, then they cannot be happy."
This can be diagrammed:
SFP -> not H (which would be diagrammed "H" with a slash through it)
When taking the contrapositive, you reverse and negate, so the opposite of "not happy" is "happy" and the opposite of "SFP" is "not SFP."
H -> not SFP (which would be diagrammed SFP with a slash through it)
This contrapositive is Answer E.
You don't really need the third statement in the stimulus to get the answer, but it's worth examining.
The third sentence of the stimulus is basically saying "if people can be happy, then their financial problems are solved."
In this case, having one's "financial problems solved" is just another way of saying that one doesn't have financial problems (anymore). In other words, once a problem is solved it is no longer a problem.
As such, the third sentence could also be diagrammed:
H -> not FP (which would be diagrammed "FP" with a slash through it)
You may notice that this statement mentioned "financial problems" in general rather than specifically "serious financial problems," but that is not a problem. Since financial problems include serious financial problems, if all your financial problems are solved, then so are your serious ones.