Solutions Quantifiers2 2: Difference between revisions

Latest revision as of 00:08, 15 November 2013

Sentence: Ramon signs every sculpture he makes.

Universal Quantifier

∀x ((sculpture(x) ∧ make(ramon, x)) ⊃ sign(ramon, x))

Paraphrse: "For every thing x, if x is a sculpture and x is made by Ramon then x is signed by Ramon."

We use the name constant ramon for both the name (Ramon) and the personal pronoun he that referes to Ramon.

In restricted quantifier notation

∀x ((sculpture(x) ∧ make(ramon, x)) : sign(ramon, x))

Here, the N' is "sculpture he makes" and therefore its translation appears in the part before the colon.

@@ Line 1: / Line 1: @@
-'''Ramon signs every sculpture he makes.'''
+Sentence: ''Ramon signs every sculpture he makes.''
 '''Universal Quantifier'''
-∀x (SCULPTURE (x) & MAKE (r, x) → SIGN (r, x))
+&forall;''x'' (('''sculpture'''(''x'') &and; '''make'''('''ramon''', ''x'')) &sup;  '''sign'''('''ramon''', ''x''))
-''"For every thing x, if x is a sculpture and x is made by Ramon (r) then x is signed by Ramon (r)."''
+Paraphrse: ''"For every thing ''x'', if ''x'' is a sculpture and ''x'' is made by Ramon then ''x'' is signed by Ramon."''
+We use the name constant '''ramon''' for both the name (''Ramon'') and the personal pronoun ''he'' that referes to Ramon.
-Since Ramon ''makes'' and ''signs'' the sculptures, the corresponding variables are (r, x).
+'''In restricted quantifier notation'''
+&forall;''x'' (('''sculpture'''(''x'') &and; '''make'''('''ramon''', ''x'')) :  '''sign'''('''ramon''', ''x''))
-'''Restricted Quantifier'''
+Here, the N' is "sculpture he makes" and therefore its translation appears in the part before the colon.
-[Every x: SCULPTURE (x) & MAKE (r, x)] SIGN (r, x)
-Here, the N' is "sculpture he makes" and therefore belongs in square brackets together with the Quantifier ''every''.
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