KA-0146Reading a logical statement precisely
3 points, difficulty 1 of 3Level 5–6about 60sSuppose it is true that some birds cannot fly. Which of these must also be true?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
How few birds could some be?
2The strategy
Some means at least one, and nothing more. Test each choice against the smallest situation the statement allows: exactly one bird in the whole world that cannot fly.
3The full solution
If exactly one bird cannot fly, then it is false that all birds can fly - but every other choice would also have to be false.
Solution
The reliable way
Some means at least one, and no more than that. Test each choice against the case where exactly one bird cannot fly and every other bird can. No birds can fly is false there. All birds can fly is false there. Most birds cannot fly is false there. Exactly one bird cannot fly happens to be true there but would be false if two birds could not fly, so it is not guaranteed. Not all birds can fly is true in every case allowed by the statement. The transferable idea: to test must be true, find the weakest situation the statement allows and check each choice against it.
The elegant way
Some A are not B is precisely the negation of all A are B, so the two are equivalent and nothing stronger follows.
Why this is on the test: Some, most and all are read interchangeably by students under time pressure, and every wrong choice here is one of those readings.