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logic_problems - 1 Represent the following English...

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1. Represent the following English sentences in First Order Logic. (a) An uncle is the brother of someone’s parent or the husband of someone’s parent’s sister. (b) Richard is Peter’s Dad. (c) Jan is Richard’s sister. (d) Jim is Jan’s husband. Prove, using proof by contradiction and resolution, that Jim is Peter’s uncle. 2. Some professors are long winded. If a professor is long winded, then there is a class that she/he teaches in which someone gets bored. People who are bored in a class drop it. Prove using First Order Logic that someone will drop some class. 1
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Solutions 1. First, let us define our predicates. The predicate UncleOf ( x, y ) is true if x is the uncle of y . The predicate BrotherOf ( x, y ) is true if x is y ’s brother, ParentOf ( x, y ) is true if x is y ’s parent and SisterOf ( x, y ) is true if x is y ’s sister. Now, let us express the knowledge in First Order Logic. (a) 1. x, y, zBrotherOf ( z, y ) ParentOf ( y, x ) UncleOf ( z, x ) 2. w, x, y, zParentOf ( y, x ) SisterOf ( w, y ) HusbandOf ( z, w ) UncleOf (
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