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Using the predicate symbols shown and appropriate quantifiers, write each English language statement in predicate logic. The domain is the whole...
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In 1,2,3 examples:

  • x is the person who is being fooled so shouldn't it be can-be-fooled(x,t) instead of can-fool(x,t). I mean doesn't it change the whole meaning.
  • Say I understood 1 so shouldn't 2 be similar or vice versa?

In 4 example :

  • I don't understand why did we use OR operator here


As far as I know the in case of implies , L.H.S is the information and the system based on this information produces R.H.S the inference.


Please make me understand all the above four examples in dept and also the doubts I've asked.

Thank you in advance.

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Using the predicate symbols shown and appropriate quantifiers, write each English
language statement in predicate logic. The domain is the whole world. In the
definition of a predicate, the variables are placeholders. They will get instantiated
within the scope of the quantifiers. 3 points (1 point each)
P(x) is "x is a person."
T(x) is "x is a time."
F(x,y) is "x is fooled at y."
1. You can fool some of the people all of the time.
a. x Vt person(x) Atime(t) + can-fool(x,t)
2. You can fool all of the people some of the time.
a. Vx 3t (person(x) -> time(t) Acan-fool(x,t))
3. You can't fool all of the people all of the time.
a. Vx 3t (person(x) Atime(t) -> ~ can-fool(x,t)

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There are exactly two purple mushrooms.
(Ex) (Ey) mushroom (x) ^ purple (x) ^ mushroom (y) ^ purple (y) ^ ~ (x=y) * (Az)
(mushroom (z) ^ purple (z) ) => ((x=z) v (y=z))

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