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sit192 ass1

# sit192 ass1 - SIT192 ASSIGNMENT 1 1(i P(rs(ii s(pq(iii(rq...

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SIT192 ASSIGNMENT 1 1. (i) ¬P (r s) ∧ ∧ (ii) s→(p q) (iii) (r ¬q) → ¬p (iv) (r ¬s) → (¬p ¬q) 2. (i) They drink, or they read and study (ii) If they don’t read, they don’t eat (iii) They study and read if and only if they eat or drink (iv) They read and don’t drink if they don’t eat 3. (i) P q ¬q p ¬q (p ¬q) q T T F T T T F T T T F T F F F F F T T F (ii) P q ¬p p q ¬(p q) ¬p → ¬(p q) T T F T F T T F F F T T F T T F T T F F T F T T (iii) P q r ¬r p q (p q) ↔ ¬r T T T F T F T T F T T T T F T F F T T F F T F F F T T F F T F T F T F F F F T F F T F F F T F F 4. (i) p ¬(p q) ≡ p ¬q LHS ≡ p ¬(p q) ≡ p (¬p ¬q) ≡ (p ¬p) (p ¬q) ∧ ∨ ≡ T (p ¬q) ∧ ∨ ≡ p ¬q ≡ RHS (ii) p ¬(¬q r) ≡ (p q) (p ¬r) ∧ ∨ ∧ LHS ≡ p ¬(¬q r) ≡ p (q ¬r) ∧ ∨ ≡ (p q) (p ¬r) ∧ ∨ ∧

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≡ RHS (iii) (p q) → p ≡ T LHS ≡ (p q) → p
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sit192 ass1 - SIT192 ASSIGNMENT 1 1(i P(rs(ii s(pq(iii(rq...

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