l15soln

# l15soln - CS 245 Winter 2009 Lecture 15 Suggested Exercises...

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CS 245 Winter 2009 Lecture 15 – Suggested Exercises SOLUTION SET 1. Formalize the following sentences in predicate logic with equality. Show the English phrases that your predicates and functions represent. (a) There are three cars in the parking lot. (b) The only one who made it to school in the snow storm was George. (c) The only person who could be the CEO is George’s daughter. (d) The person who won the award is the tallest person on some university basketball team. Soln: (a) x,y,z car ( x ) inlot ( x ) car ( y ) inlot ( y ) car ( z ) inlot ( z ) ∧¬ ( x = y ) ∧¬ ( x = z ) ∧ ¬ ( y = z ) where car ( x ) – means x is a car inlot ( x ) – means x is in the parking lot (b) SSS ( George ) ∧ ∀ x SSS ( x ) ( x = George ) where SSS ( x ) – means that x made it to school in the snow storm. (c) x CEO ( x ) x = daughter ( George ) where CEO ( x ) – means that x could be the CEO. daughter ( x ) – is the daughter of x . (d) x award winner ( x ) ∧∃ t onteam ( x,t ) ∧∀ p onteam ( p,t ) ∧¬ ( x = p ) taller ( x,p ) where award

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l15soln - CS 245 Winter 2009 Lecture 15 Suggested Exercises...

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