Support Roberta is irritable only when she is tired, and Support loses things only when she is tired. █████ ███ ███ ████ ███████ ███ ████ ███ ███ ████ ████ ███ █████ ███ ██ ██████ █████████ ██████████
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 ██ ████ ██
infers from a ███████████ ███████ █████████ ███ ███████ ████ █████████ ██████ ███████
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takes a necessary █████████ ███ █████████ ██████ ██████ ██ ██ █ ██████████ █████████
takes a necessary █████████ ███ █████████ █████ █████████ ██ ██ █ ██████████ █████████