Look, Costa Coffee, it's really quite simple.
Let:
l(x) | x is lactose intolerant |
s(x) | x wants soy milk in their cappuccino |
c(x) | x wants chocolate powder on top |
Then:
∀x[ l(x) → s(x) ∧ ¬c(x) ] | |
∀x[ l(x) → ¬c(x) ] | (simplification) |
But:
∃x[ ¬l(x) ∧ s(x) ] | |
¬ ∀x[ ¬[ ¬l(x) ∧ s(x) ] ] | (negation of quantified statement) |
¬ ∀x[ l(x) ∨ ¬s(x) ] | (DeMorgan's law) |
¬ ∀x[ s(x) → l(x) ] | (implication) |
So:
∴ ¬ ∀x [ s(x) → ¬c(x) ] | (hypothetical syllogism) |
I just prefer soy, ok?
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