Explanation of the Solution to Free Lunch Challenge 3

Congratulations again to Xayla Wilson for winning the free lunch challenge.  I thought some of you might be interested in the explanation to the problem.  See below for a reprint of the problem followed by its solution.

Logical Reasoning

Everyone who is compassionate is kind, and someone who has experienced life’s challenges is invariably compassionate. Jeremy is kind, so he has experienced life’s challenges.
Which one of the following exhibits a pattern of flawed reasoning most similar to that exhibited above?

(A) Roberta is a highly productive person. Every person who is motivated is highly productive, and every person who is organized is motivated. Therefore, Roberta is very organized.
(B) Nice people are always sympathetic people, and those who have experienced hardships always end up being nice. Betsy is not a sympathetic person, so Betsy has not experienced hardships.
(C) Almost everyone who loves black and white films is a movie buff, and all movie buffs enjoy popcorn. Sasha does not love black and white films, so Sasha probably does not enjoy popcorn.
(D) Patience requires an even temperament, and being a good parent certainly requires patience. James has no patience, so James is not a good parent.
(E) Successful entrepreneurs are either confident or experienced. Yoshi is a successful entrepreneur, and he is not experienced. Therefore, Yoshi is confident.

Solution:

The given argument contains two conditional statements:
1. Everyone who is compassionate is kind. (C → K)
2. Someone who has experienced life’s challenges is invariably compassionate. (E → C)
We can connect these conditionals: E → C → K
From this chain we can see that someone who has experienced life’s challenges is kind: E → K
Notice that the conclusion of the argument is the reverse of this. If Jeremy is kind, then he has experienced life’s challenges: K → E
This is an invalid reversal of the logic. To get a sense of what that means, consider this:
If we know that If Tony wins the prize, he’ll be happy (P → H), can we infer that if Tony is happy, it means he won the prize (H → P)? It may be tempting to say yes, but we cannot infer that (we can’t say it for sure) because perhaps Tony is happy for a different reason (he got engaged, he got a raise at work, etc.).

In selecting our answer, we want to look for a choice that makes the same invalid reversal.
Answer (A): CORRECT
Every person who is motivated is highly productive. (M → HP)
Every person who is organized is motivated. (O → M)
These connect to give: O → M → HP
So we know: O → HP
The argument uses reversed logic to make a conclusion about Roberta. Because she is highly productive, she is organized: HP → O
This is the same flaw that appeared in the original argument, so this is the correct answer. This answer is a bit tricky because the argument is in a different order. However, we’re tasked with finding an argument with the same flawed logic. The order is irrelevant.
Answer (B):
Nice people are always sympathetic people. (N → S)
Those who have experienced hardships always end up being nice. (EH → N)
These connect to give: EH → N → S
So we know: EH → S
The argument uses a correct contrapositive to makes its conclusion about Betsy. Betsy is not sympathetic, so Betsy has not experienced hardships: -S → -EH
This argument has no flaw.
Answer (C):
We can tell immediately that this argument does not contain the same conditional logic flaw as the original because two out of three statements in this argument aren’t even conditional statements:almost everyone who loves black and white films, and Sasha probably does not enjoy popcorn.
Answer (D):
Patience requires an even temperament. (P → ET)
Being a good parent certainly requires patience. (BGP → P)
These connect to give: BGP → P → ET
The argument uses a correct contrapositive to make its conclusion about James. James has no patience, so James is not a good parent: -P → -BGP
This argument has no flaw.
Answer (E):
This argument is based on either/or logic, which is different from the logic used in the original argument. Furthermore, this argument is not flawed. If Yoshi is not experienced he must be confident.