Thog Problem
Given the following combinations of shapes and colors:
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The experimenter makes the following statement:
“I am thinking of one color (black or white) and one shape (square or circle). Any figure that has either the color I am thinking of, or the shape I am thinking of, but not both, is a THOG. Given that the black square is a THOG what, if anything, can you say about whether the other figures are THOGS?”
Select the THOG by clicking on one of the shapes above
Let Whiteness = 0 and Blackness = 1
Let Squareness = 0 and Circular = 1
Then you can describe your THOG with two bits, one for color and one for shape
XOR with 1 1 to find the opposite THOG.
Nice. I never thought about it like that
Yeah, so the right shape must be either a white square or black circle. As above, the other THOG is a black square. If the right shape is a white square, then the black circle is neither a THOG or the right one. The opposite is also true.
This problem just screamed “Boole” out to me!
Err black square and white circle*