Bunuel wrote:
Elena: While I was at the dog show, every dog that growled at me was a white poodle, and every white poodle I saw growled at me.
Which one of the following can be properly inferred from Elena’s statement?
(A) The only white dogs that Elena saw at the dog show were poodles.
(B) There were no gray poodles at the dog show.
(C) At the dog show, no gray dogs growled at Elena.
(D) All the white dogs that Elena saw growled at her.
(E) Elena did not see any gray poodles at the dog show.
OFFICIAL EXPLANATION
(A) No. The passage does tell us that a dog growled at Elena if and only if it was a white poodle. However, this does not preclude the possibility of other white dogs being at the show—they just didn’t growl at Elena.
(B) No. The clause “
every dog that growled at me was a white poodle” contains an embedded if-then statement: if a dog growled at me, it was a white poodle. This in turn can be diagrammed as follows:
G—>WP
This diagram allows gray poodles; they just can’t growl at Elena.
(C) Yes. The clause “
every dog that growled at me was a white poodle” contains an embedded if-then statement: if a dog growled at me, it was a white poodle. This in turn can be diagrammed as follows:
G—>WP
Now, if a particular dog growled at Elena, it must be a white, not gray, poodle.
It may help to apply the contrapositive to the above diagram: ~WP—>~G. Now, a gray dog is not a white poodle. Hence, the hypothesis of the if-then statement ~WP—>~G is satisfied. Therefore, the conclusion ~G must follow—that is, no gray dog growled at Elena.
(D) No. The clause “
every dog that growled at me was a white poodle” contains an embedded if-then statement: if a dog growled at me, it was a white poodle. This in turn can be diagrammed as follows:
G—>WP
Now, if a particular dog growled at Elena, it must be a white poodle. Hence, it does not follow that all white dogs growled at Elena unless there were only white poodles at the dog show.
(E) No. The clause “
every dog that growled at me was a white poodle” contains an embedded if-then statement: if a dog growled at me, it was a white poodle. This in turn can be diagrammed as follows:
G—>WP
This diagram allows gray poodles; they just can’t growl at Elena.
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