Book Question Set #1: Ertel, Chapter 2: Propositional Logic
... d. ( A IMPLIES B ), where A and B are a propositional variable An implication that, ‘if A then B’ (also known as material implication) e. ( A EQUIVALENT-TO B ), where A and B are a propositional value A statement of equivalence where, ‘A if and only if B’ 6.) What does it mean for two propositional ...
... d. ( A IMPLIES B ), where A and B are a propositional variable An implication that, ‘if A then B’ (also known as material implication) e. ( A EQUIVALENT-TO B ), where A and B are a propositional value A statement of equivalence where, ‘A if and only if B’ 6.) What does it mean for two propositional ...
1
... (c) Prove the following by induction (on construction of formulas): if variable assignments s and s0 agree on all variables occurring in a formula φ, then |=U φ [s] iff |=U φ [s0 ] for all formulas φ and interpretations U. (You may assume that the language has only the connectives ¬ and → and that ∀ ...
... (c) Prove the following by induction (on construction of formulas): if variable assignments s and s0 agree on all variables occurring in a formula φ, then |=U φ [s] iff |=U φ [s0 ] for all formulas φ and interpretations U. (You may assume that the language has only the connectives ¬ and → and that ∀ ...
Ch1 - COW :: Ceng
... Extend I to all formulas: 1. I(T) = 1 and I() = 0. 2. I(A1 ... An) = 1 if and only if I(Ai) = 1 for all i. 3. I(A1 ... An) = 1 if and only if I(Ai) = 1 for some i. 4. I(A) = 1 if and only if I(A) = 0. 5. I(A B) = 1 if and only if I(A) = 0 or I(B) = 1. 6. I(A B) = 1 if and only if I(A) ...
... Extend I to all formulas: 1. I(T) = 1 and I() = 0. 2. I(A1 ... An) = 1 if and only if I(Ai) = 1 for all i. 3. I(A1 ... An) = 1 if and only if I(Ai) = 1 for some i. 4. I(A) = 1 if and only if I(A) = 0. 5. I(A B) = 1 if and only if I(A) = 0 or I(B) = 1. 6. I(A B) = 1 if and only if I(A) ...
