Syntax 1 Wiki: Week 3: Difference between revisions

Revision as of 09:56, 9 November 2020

Exercise 1 Kim snores.

Check your answer

< >

1. Kim snores.

2. Kim likes Robin.
3. Kim talked to the student.
4. Kim showed Hessen to Robin.
5. Kim handed Robin the apple.

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 == Valence ==
-'''Exercise 1'''  For I('''cat<sup>1</sup>''') and I('''lilly'''), specify one plausible value each so that the formula '''cat<sup>1</sup>(lilly)''' becomes true in M.
+'''Exercise 1'''  Kim <u>snores</u>.
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 Check your answer
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-I('''cat<sup>1</sup>''') = {<''cat1''>,<''cat2''>,<''cat3''>}
+< >
-For I('''lilly'''), each of the following 3 values will now make '''cat<sup>1</sup>(lilly)''' true in M:<br>
-a. I('''lilly''') = ''cat1'' , or<br>
-b. I('''lilly''') = ''cat2'' , or<br>
-c. I('''lilly''') = ''cat3'' .
-We prove this for case (b):
-. [[<nowiki />'''cat'''<sup>1</sup>('''lilly''')]]<sup>M</sup> = 1 iff <[[<nowiki />'''lilly''']]<sup>M</sup>> &isin; I('''cat<sup>1</sup>''')<br>
-. iff <I('''lilly''')> &isin; I('''cat<sup>1</sup>''')<br>
-. iff <''cat2''> &isin; {<''cat1''>,<''cat2''>,<''cat3''>}<br>
-Hence: since (3) is the case, so are (2) and the righthand side of (1). Finally, since the righthand side of (1) is the case, the lefthand side is the case as well. Hence [[<nowiki />'''cat'''<sup>1</sup>('''lilly''')]]<sup>M</sup> is true in model M. That is what we intended to prove!
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