Four Defensible Odd Ones Out
During a word-study block, four students each argue for a different odd one out from the same four words written on the board: BAT, PENGUIN, OSTRICH, BUTTERFLY. The teacher sets two ground rules before anyone votes. First, the other three words must share a property that the chosen word lacks. Second, that shared property must be stated positively ("are vertebrates") rather than as a leftover ("are not butterflies").
Priya picks BUTTERFLY: the others are vertebrates. Devon picks BAT: the others are birds. Sam picks PENGUIN: the others live on land and never enter water. Ana picks OSTRICH: the others can either fly or swim.
Every claim is factually accurate, so the class cannot settle the argument by checking facts. The teacher asks the group to rank the four claims by strength, to say exactly what makes one claim tighter than another, and to test whether adding a fifth word would break the ranking.
1. For each of the four claims, state the shared property of the remaining three words and classify it as a single positive property, a negative property, or a disjunction. Then rank the claims from strongest to weakest.
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Priya: bat, penguin, and ostrich are vertebrates. One property, stated positively, naming a natural biological class.
Devon: penguin, ostrich, and butterfly are birds. Same type of property as Priya's, only narrower.
Sam: bat, ostrich, and butterfly are terrestrial animals. The clause "never enter water" is redundant wording, not a second criterion, so this is still a single positive property - but a broad one that groups a mammal, a bird, and an insect.
Ana: bat flies, penguin swims, butterfly flies - the leftover three share only the disjunction "flies or swims." Different members satisfy it for different reasons, so no one property unites them.
Ranking: Devon and Priya tie at the top (each names a single natural class), Sam next (true and positive, but broad and padded with a negative clause), Ana last. The Devon–Priya tie is not a flaw in the task: those rules differ in narrowness, not in kind, so the exam would have to prefer one explicitly.
2. Ana objects that her rule covers the remaining three words exactly, so it should count. Write a reply that explains why a disjunction is weaker than a single shared property even when the disjunction is true.
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The reply should not dispute Ana's facts - all four birds-and-beasts claims are true. The objection is structural.
A classification earns its keep by unifying the group: one property, held by every member, for the same reason. Ana's rule gives three different reasons - the bat qualifies by flying, the penguin by swimming. That means the rule does not actually say what the three have in common; it lists what each can do.
The practical test is predictive. Ask what a new word would do to the group. Add SALMON: Ana's rule absorbs it (it swims), just as it would absorb nearly any animal, because "fly or swim" is elastic. A rule that cannot exclude anything has stopped classifying.
A second test is post-hoc repair. If disjunctions are allowed, any odd-one-out claim can be rescued after the fact by bolting on another "or," so the claim wins no argument; it merely survives.
3. Propose one additional word that makes Devon's claim fail while leaving Priya's claim intact. Explain exactly what happens to each claim and to the ranking.
Read the worked answer
SALMON works.
Devon chose BAT and said the remaining three are birds. With SALMON added, the remaining group becomes penguin, ostrich, butterfly, salmon - and salmon is a fish, so "are birds" is false. Devon's claim collapses.
Priya chose BUTTERFLY and said the remaining three are vertebrates. With SALMON added, the remaining group is bat, penguin, ostrich, salmon - a mammal, two birds, and a fish - all vertebrates. Priya's claim survives unchanged.
Sam's claim also fails: salmon enter water, so "live on land and never enter water" no longer describes the leftover group. Ana's disjunction survives, and its survival is the point - it now covers bat (flies), penguin (swims), salmon (swims), so it has grown more permissive, not more informative.
Revised ranking: Priya alone at the top, Sam and Devon eliminated, Ana retained but weaker than before, since her rule now spans four unlike animals.