KA-0099Reading a logical statement precisely
4 points, difficulty 2 of 3Level 3–4about 60sAll the red boxes are heavy. Box X is not heavy. What must be true?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Suppose box X were red. What then?
2The strategy
Assume the thing you want to test. If assuming it forces something you know is false, it cannot be true, and the opposite must be.
3The full solution
If X were red, the rule would make it heavy. But X is not heavy. So X cannot be red.
Solution— no shortcut on this one
Suppose box X were red. The rule says all red boxes are heavy, so X would be heavy - but we are told it is not. The assumption breaks, so X is not red. Nothing follows about what colour it is instead: the rule is silent on that. The transferable idea: from all A are B and this is not B, you may conclude this is not A, and nothing more.
Why this is on the test: Reading a rule backwards is the most common logical slip on the paper, and going one step too far by naming a colour is the second.