EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...

Translating English to propositional logic
• Because English has compound propositions, it’s sometimes possible to
phrase these propositions as formal propositional expressions and to build
truth tables therefrom. This is a bit inexact, and there is very often more
than one way to do it. There’s a way to test whether two translations are
equivalent, though.
• Example from text: “You cannot ride the roller coaster if you are under 4
feet tall unless you are older than 16.”
• We find the basic propositions in this informal expression and assign them
propositional variables: “you can ride the roller coaster” is assigned r,
”you are under 4 feet tall” is assigned u, and ”you are over 16” is assigned
o. Then the English sentence before ”unless” would translate as ”u → ¬r”.
• But what about the “unless” part Here o qualifies u in the sense that if
somebody is under 6 feet, and not over 16, then they cannot ride. So a
correct translation is
(u ∧ ¬o) → ¬r.
• How about (u → ¬r) ∧ (o → r) Is this the same What does “same”
mean To be continued in the next lecture.
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