section_3.07_answers

section_3.07_answers - PHIL12A Section answers 7 March 2011...

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PHIL12A Section answers, 7 March 2011 Julian Jonker 1 Revision problems 1. Translate the following sentences into FOL, devising your own names and predicates where necessary: (a) Block c is a tetrahedron just in case block a is in between block c and block d. Tet(c) Between(a,c,d) (b) Neither block a nor block b is to the left of e or to the right of c. ¬ (LeftOf(a,e) RightOf(a,c)) ∧¬ (LeftOf(b,e) RightOf(b,c)) or ¬ LeftOf(a,e) ∧¬ LeftOf(b,e) ∧¬ (RightOf(a,c) ∧¬ RightOf(b,c) (c) John is his father’s son, provided he is a human being. Human(john) john=son(father(john)) 2. Is ¬ ( A B ) C a tautological consequence of ¬ ( ¬ A ∧ ¬ B ∧ ¬ C ) ? Using the short cut: ¬ ( ¬ A ¬ B ) C ¬ ( A B ) C T F T T F T F F T F T F T F F F F F T Tx F F Tx F T F T F F F F F 1
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3. Put the following sentence into Negation Normal Form, showing your working through a chain of equiv- alences: ( ¬ ( ¬ A ∨ ¬ B ) A ) ( ¬¬ D ∧ ¬ ( C ∨ ¬ D )) .
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