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PHIL12A Section answers, 14 March 2011 Julian Jonker 1 How much do you know? 1. Use truth tables to check whether the following equivalences hold: (a) P Q ⇔ ¬ Q → ¬ P P Q P Q ¬ Q → ¬ P T T T T T F T T F T T F T F F T F F F T F T F T T F T T T F F F F T F T F T T F (b) P Q ( P Q ) ( Q P ) P Q ( P Q ( P Q ) ( Q P ) T T T T T T T T T T T T T F T F F T F F F F T T F T F T T F T T F T F F F F F T F F T F T F T F 2. Translate the following arguments into the Blocks language, and then write informal proofs of their validity. Explicitly notes any inferences using modus ponens , biconditional elimination, or conditional proof. 1

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(a) (Based on Ex 8.6) 1 a is a large tetrahedron or a small cube. 2 b is not small. 3 If a is a tetrahedron or a cube, then b is large or small. 4 a is small or b is large. Translation: 1 (Tet(a) Large(a)) (Cube(a) Small(a)) 2 ¬ Small(b) 3 (Tet(a) Cube(a)) (Large(b) Small(b)) 4 Small(a) Large(b) By premise 1, either a is a large tetrahedron or a small cube. Let’s consider each case. Case:
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