Support Roberta is irritable only when she is tired, and Support loses things only when she is tired. Since Support she has been yawning all day, and has just lost her keys, Conclusion she is almost certainly irritable.
The author concludes that Roberta is probably irritable. He supports this with the following premises:
(1) If Roberta is irritable, then she is tired.
(2) If Roberta loses things, then she is tired.
(3) Roberta is yawning and she lost her keys.
This is the cookie-cutter flaw of confusing necessary and sufficient conditions. Roberta yawning might suggest that she’s tired, but we also know that if she loses something, then she is tired. Because she lost something (her keys), the author could correctly conclude that Roberta is tired. But instead, he concludes that she is irritable.
The argument establishes that Roberta is tired, but the author treats “tired” as sufficient for “irritable.” According to premise 1, “tired” is necessary. In other words, Roberta could be losing things and therefore be tired but still not be irritable.
The reasoning above is flawed in that it
infers from a correlation between tiredness and yawning that tiredness causes yawning
This is the cookie-cutter flaw of assuming correlation proves causation. The author doesn’t make this mistake. He says that Roberta is yawning, but never assumes that this is caused by her tiredness. Because she lost her keys, we know that Roberta is indeed tired.
assumes the conclusion that it sets out to prove
This is the cookie-cutter flaw of circular reasoning, where the argument’s conclusion merely restates a premise. The author doesn't make this mistake. His premises may not support his conclusion well, but they are distinct from his conclusion.
generalizes on the basis of a single instance
This is the cookie-cutter flaw of hasty generalization, where an argument draws a broad conclusion from too little evidence. The author doesn’t make this mistake. He draws a conclusion about Roberta based on evidence about Roberta; he never generalizes about anyone else.
takes a necessary condition for Roberta's losing things to be a sufficient condition
This is the cookie-cutter flaw of confusing necessary and sufficient conditions. The author does make this mistake, but not in the way that (D) describes. He thinks that Roberta being tired is sufficient for her being irritable, not that it’s sufficient for her losing things.
takes a necessary condition for Roberta's being irritable to be a sufficient condition
The argument says that Roberta lost her keys, which means that she’s tired. The author then treats “tired” as sufficient for Roberta’s being irritable, but according to the premises, “tired” is necessary. Roberta could be tired but not irritable.
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