Mark V. Lawson's An introduction to logic [Lecture notes] PDF

By Mark V. Lawson

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Of pn or ¬pn where pi is chosen if vi = T and ¬pi is chosen if vi = F . I shall call A a basic conjunction corresponding to the pattern of truth values v1 , . . , vn . The truth table of A is the given truth function. Step 3. Suppose that we are given now an arbitrary truth function not covered in steps 1 and 2 above. We construct a wff A whose truth table is the given truth function by taking a disjunction of all the basic conjunctions constructed from each row of the truth function that outputs T .

We use our truth tables above to evaluate this expression in stages T → (F ↔ F ), T → T, T. 2. If the compound proposition A consists of n atoms then there are 2n possible truth assignments. p⊕q F T T F 12 CHAPTER 1. PROPOSITIONAL LOGIC We may draw up a table, also called a truth table, whose rows consist of all possible truth assignments along with the corresponding truth value of A. We shall use the following pattern of assignments of truth values: ... T T T ... T T F ... T F T ... T F F ... F T T ...

T T F ... T F T ... T F F ... F T T ... F T F ... F F T ... F F F ... ... 3. Here are some examples of truth tables 1. The truth table for A = ¬(p → (p ∨ q)). p T T F F q T F T F p ∨ q p → (p ∨ q) T T T T T T F T A F F F F 2. The truth table for B = (p ∧ (p → q)) → q. 3. SEMANTICS OF PROPOSITIONAL LOGIC 13 3. The truth table for C = (p ∨ q) ∧ ¬r. p T T T T F F F F q T T F F T T F F r T F T F T F T F p ∨ q ¬r T F T T T F T T T F T T F F F T C F T F T F T F F 4. Given the wff (p ∧ ¬q) ∧ r we could draw up a truth table but in this case we can easily figure out how it behaves.

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An introduction to logic [Lecture notes] by Mark V. Lawson


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