Concept
Why is the assertion X ∧ ¬ Y ∧ ¬ ( Z ⇒ X ) impossible?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Q and replace it with X , thus making my asser- tion: “ X ∧ ¬ Y ∧ ¬ ( Z ⇒ X ) .” Now what is/are the solutions? Now it’s impossible, and if you study the previous item, you’ll see why. The only way that item 24 could be true was if the con- clusion of the implication (namely, Q ) was false. But X had to be true. So whether X is true or false in this new assertion, some- thing will go haywire: either it’ll be true and the third and-ed thing will be false, or else it’ll be false and the first and-ed thing will be false. There’s no way the professor could be telling the truth here. At the time of this writing, all professors are human, and that’s what I’ll be assuming in these ex- ercises."
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