Lecture Notes 7 - DISCUSSION OF FIRST HOMEWORK...

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37 DISCUSSION OF FIRST HOMEWORK ASSIGNMENT… GREATEST PROBLEMS: 13, 14, BONUS... SYMBOLIZATION CONTINUED… SPECIAL CASE: p unless q = if not q then p = ~ q p SANTA WILL NOT BE ARRESTED UNLESS THE ELVES TIP OFF THE COPS ~ E ~ S SYMBOLIZING p IF AND ONLY IF q ( p <--> q ) VARIANT p JUST IN CASE q NOTE: THERE ARE MANY SEMANTICALLY EQUIVALENT, BUT SYNTACTICALLY DIFFERENT WAYS OF CORRECTLY SYMBOLIZING MANY ENGLISH SENTENCES IN THE LANGUAGE OF SL. NOT BOTH p AND q :: ~ (p & q) :: ~ p V ~ q NEITHER p NOR q :: ~ (p V q) :: ~ p & ~ q p UNLESS q :: ~ q p :: p V q p ONLY IF q :: p q :: ~ q ~ p p IF AND ONLY IF q :: p <--> q :: (p q) & (q p) COMPLEX TRANSLATION EXAMPLES MRS. CLAUS WILL NOT BE ARRESTED IF SANTA IS, BUT RUDOLPH WILL GO INTO HIDING. RUDOLPH WILL GO INTO HIDING IF EITHER SANTA OR MRS. CLAUS IS
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38 ARRESTED. ONLY IF SANTA IS ARRESTED WILL RUDOLPH GO INTO HIDING, BUT IF SANTA IS ARRESTED MRS. CLAUS WILL BE ARRESTED. SANTA WILL BE ARRESTED ONLY IF THE ELVES TIP OFF THE COPS AND RUDOLPH GOES INTO HIDING
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