Consider the following predicates over the set U of all UBC students: P(x): x is

Question

Consider the following predicates over the set U of all UBC students: P(x): x is doing a BA in philosophy. S(x): x speaks Swahili. H(x): x plays hockey. W(x): x likes watching the Weather Channel. K (x, y): person x knows (is acquainted with) person y. Translate each of the following predicate logic statements into English. Try to make your English translations as natural sounding as possible. (a) exist x elementof U, forall z elementof U, P(z) rightarrow K (x, z) (b) forall x elementof U, exist y elementof U, forall z elementof U, K (x, y) logicaland [(K (y, z) rightarrow ~ K(z, x)]

Explanation / Answer

3(a) Every swahili speaking hockey player knows a student who studies philosophy.

3(b) There is a student who does not know any philosophy student who knows Marguerite.

Explanation:

These are the key to symbols for translating the predicates in to english.

~ = negation
& = conjunction
--> = conditional implication
E = existential quantifier
A = universal quantifier

For example take a scenerio

There is no free lunch.
~Ex[F(x) & L(x)]
F(x) = x is free
L(x) = x is lunch

Here ~ = negation indicates negitivity

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