This week, we learned about the difference between
natural language and idiom and its logic interpretation into symbols.
It was very interesting that "unless" could
be exchanged into "if not" but the position should be switched for
the symbolic translation.
In professor's slides,
Don't knock it unless you've tried it
= Don't knock it if not you've tried it
= If not you've tried it, then don't knock it
¬ T ⇒ ¬K ≡
K ⇒ T
In idiom parts, it was amusing fact that just the
subtle difference between all and some could change the choice of '∧' and '⇒' in symbolic interpretation such as
Every D that is
a P is also a Q
∀x ∈ D,
P(x) ⇒ Q(x)
Some D that is a P is also a Q
∃x ∈ D,
P(x) ∧ Q(x)
Also, we learned about how to negate and parse a
logical expression. I think the negation
is very important skill to prove counterexamples and should practice as many as
I could.
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