Among a sample of diverse coins from an unfamiliar country, each face of any coin portrays one of four things: a judge's head, an explorer's head, a building, or a tree. ██ █████████ ███ ██████ █ █████████ ██████████ ████ ████ ██ ████ ████ █████ ██ ████ █████ ███ ████ ███ █████ ██ ███ ██████ ████ █ ███████ ████ ██ ███ ████ ████ █ ████ ██ ███ ██████
The stimulus can be diagrammed as follows:
If you have a judge’s head on one side, you must have a tree on the other side.
If you have an explorer’s head on one side, you can have a building or a tree on the other side.
If you have a building on one side, you can have a building, a tree, or an explorer’s head on the other side.
If you have a tree on one side, you can have a tree, a judge’s head, an explorer’s head, or a building on the other side.
If the statements above are █████ █████ ███ ██ ███ █████████ ████ ██ ████ ██ ███ █████ ██ ███ ███████
All those with ██ ██████████ ████ ██ ███ ████ ████ █ ████████ ██ ███ ██████
This could be false. A coin with an explorer’s head on one side could have a building OR a tree on the other side.
All those with █ ████ ██ ███ ████ ████ █ ███████ ████ ██ ███ ██████
This could be false. Any coin with a tree on one side could have a tree, a building, an explorer’s head, or a judge’s head on the other side. (We know JH→T, but it would be confusing the sufficient and necessary conditions to claim that T→ JH).
None of those ████ █ ████ ██ ███ ████ ████ ██ ██████████ ████ ██ ███ ██████
This could be false. A coin with a tree on one side can have a tree, a building, an explorer’s head, or a judge’s head on the other side.
None of those ████ █ ████████ ██ ███ ████ ████ █ ███████ ████ ██ ███ ██████
This must be true. Any coin with a judge’s head on one side must have a tree on the other side, so a coin with a judge’s head on one side would not have a building or an explorer’s head on the other side.
None of those ████ ██ ██████████ ████ ██ ███ ████ ████ █ ████████ ██ ███ ██████
This could be false. A coin with an explorer’s head on one side could have a building or a tree on the other side.
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