Phil1001__Problem_Set_11___Answer_Key

Phil1001: Introduction to Logic Name: Fall 2021 Group: Problem Set 11: Sentences of FOL – Answer Key Due: December 6, 2021 at 11:59pm These are example solutions! With the exception of (3), your solutions may differ significantly. Ask your TA if you are uncertain of the quality of your answer. 1. (4pts) Definite Descriptions. Provide a translation into FOL of the following two definite description. Make sure to provide a translation key. (Reference: Ch. 27) a. The President of the University of Minnesota has a Philosophy B.A. ∃ x (( U ( x ) ∧ ∀ y ( U ( y ) → x = y )) ∧ P ( x )) U ( x ) : x is President of the University of Minnesota P ( x ) : x has a Philosophy B.A. b. The world’s oldest living llama was born in 1994. ∃ x (( L ( x ) ∧ ∀ y (( L ( y ) ∧ ¬ x = y ) → Y ( y, x ))) ∧ B ( x ) L ( x ) : x is a living llama Y ( x, y ) : x is younger than y B ( x ) : x was born in 1994 (…his name is Ramadan’s Arapahoe Gold aka ‘Rapper’ You can see him with his llamadad here.) 2. (3pts) Ambiguity The following sentence is ambiguous. Give two possible, logically distinct symbolizations of this sentence in FOL. Make sure to include a translation key. Additionally, explain how these two symbolizations are distinct. Mari saw only red apples at the grocery. M ( x ) : Mari saw x G ( x ) : x was at the grocery R ( x ) : x is a red apple A ( x ) : x is an apple D ( x ) : x is red ∀ x (( M ( x ) ∧ G ( x )) → R ( x )) The only things that Mari saw at the grocery were red apples. (Ie, they were out of literally everything else).