In a Carroll diagram sorting numbers by 'Even / Not Even' and 'Less than 20 / Not Less than 20,' where does the number 15 go?
AEven, Less than 20
BNot Even, Less than 20
CEven, Not Less than 20
DNot Even, Not Less than 20
15 is odd (Not Even) and 15 < 20 (Less than 20), so it goes in the 'Not Even, Less than 20' cell. You must check both attributes independently — being not even and being less than 20 are separate properties that together determine the correct cell.
Question 2 Multiple Choice
A Carroll diagram always has exactly how many cells?
ATwo cells — one for each attribute
BThree cells — yes, no, and maybe
CFour cells — each attribute has two options (yes/no), and 2 x 2 = 4
DIt depends on how many objects you are sorting
A standard Carroll diagram uses two yes/no attributes, creating a 2x2 grid with exactly four cells. Each cell represents one combination: yes-yes, yes-no, no-yes, no-no. The number of objects does not change the number of cells — cells can have many objects, one object, or be empty.
Question 3 True / False
A Carroll diagram and a two-circle Venn diagram can display the same information.
TTrue
FFalse
Answer: True
Both organize objects by two attributes. The four regions of a Venn diagram (left only, right only, overlap, outside) correspond to the four cells of a Carroll diagram. The formats are different — circles vs. grid — but the logical structure is identical. Some people find Carroll diagrams easier because the cells are clearly separated and labeled, while Venn diagrams better show the overlap visually.
Question 4 Short Answer
Why does a Carroll diagram label rows with both an attribute and its opposite (e.g., 'Red' and 'Not Red') instead of just listing 'Red'?
Think about your answer, then reveal below.
Model answer: Including the opposite makes the classification exhaustive — every object has a place. If you only listed 'Red,' you would have no designated place for non-red objects, and your sort would be incomplete. By explicitly including 'Not Red,' the Carroll diagram forces you to account for everything, including objects that lack the attribute. This is also an introduction to negation in logic: 'not red' is a meaningful category, not just the absence of a category.
The explicit negation is what makes Carroll diagrams a logic tool rather than just a sorting tool. In formal logic, negation (NOT) is a fundamental operation. Carroll diagrams train students to think in terms of 'has property X' and 'does not have property X' — which is exactly how propositions and their negations work.