Incorrect information regarding Figure 12.1 #1715
Description
Hi,
Both in the main text referring to Figure 12.1 and in the caption it is claimed "the complete set of Boolean operations". This is false. With two variables x and y there are 4 possible inputs (all combinations of true and false for x and y). For each input there are two possible outputs. This gives 2^4 = 16 possible operators. You only show 7. Some of the 16 operators are less useful than others, but you are missing, for example, the operators NAND, NOR, implication and equivalence. Among the less interesting ones are, for example, the constant true and constant false operators.
The problem is that you are not considering the outside of the two circles. A proper Venn diagram has two circles in a box, with the box denoting the universe. You now have 4 areas corresponding to the 4 possible inputs. Marking these 4 areas you can easily show the 16 different Boolean operations on two variables.
Whether you want to show these 16 operators or not is a matter of taste, but you shouldn't claim that what you have "the complete set".
Best,
Jens