Methods of Proof for Boolean Logic
... Why truth tables are not sufficient: • Exponential sizes • Inapplicability beyond Boolean connectives ...
... Why truth tables are not sufficient: • Exponential sizes • Inapplicability beyond Boolean connectives ...
1. Axioms and rules of inference for propositional logic. Suppose T
... Proof. Either (i) Sn ∈ Γ or (ii) (H, Sn ) is a rule of inference for some H ⊂ {Sj : j < n}. If (i) holds it is trivial that Γ |= Sn so suppose (ii) holds. We may suppose inductively that Γ |= H for H ∈ H. The preceding Lemma implies that Γ |= Sn . ¤ Theorem 1.1. (The soundness theorem.) Suppose Γ is ...
... Proof. Either (i) Sn ∈ Γ or (ii) (H, Sn ) is a rule of inference for some H ⊂ {Sj : j < n}. If (i) holds it is trivial that Γ |= Sn so suppose (ii) holds. We may suppose inductively that Γ |= H for H ∈ H. The preceding Lemma implies that Γ |= Sn . ¤ Theorem 1.1. (The soundness theorem.) Suppose Γ is ...
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... The action for x A is something like, “pick any x from A you want” Since a “for all” must work on everything, it doesn’t matter which you pick The action for y B is something like, “find some y from B” Since a “there exists” only needs one to work, you should try to find the one that matches ...
... The action for x A is something like, “pick any x from A you want” Since a “for all” must work on everything, it doesn’t matter which you pick The action for y B is something like, “find some y from B” Since a “there exists” only needs one to work, you should try to find the one that matches ...
STEPS for INDIRECT PROOF - Fairfield Public Schools
... triangle theorem that states all angles of an equilateral triangle are congruent.) 3) Write a ‘therefore’ statement as a conclusion that the PROVE must be TRUE. For example, “Therefore , since our assumption lead to a CONTRADICTION (or absurd statement) , then our assumption must be FALSE, and _____ ...
... triangle theorem that states all angles of an equilateral triangle are congruent.) 3) Write a ‘therefore’ statement as a conclusion that the PROVE must be TRUE. For example, “Therefore , since our assumption lead to a CONTRADICTION (or absurd statement) , then our assumption must be FALSE, and _____ ...