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MGF 1106 (4)

Lecture 3

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MGF 1106
Jordan Draper

Logic  Statement- a sentence that is either true or false o assign each statement a letter; usually p, q, or r o simple statement- one letter denoting a statement o compound statement- combining statements by using connectives Connective Symbol Name Example and ∧ conjunction p∧q or ∨ disjunction p∨q if, then → conditional p→q if and only if ↔ biconditional p↔q  ∼ = not, negates the original statement o ex. p= The sky is blue. ∼p = The sky is not blue.  Using connectives o ex. p= It’s windy. q= It rained. r= It was cold. 1. (p∨∼q) ∧ ∼r It was windy or it did not rain, and it was not cold. 2. p∨(∼q∧∼r) It was windy, or it did not rain and it was not cold. 3. ∼p∧r It was not windy and it was cold. 4. ∼(p∧r) It is not true that it was windy and it was cold.  Quantifiers- all, some, none, etc. o ex. p= All cats are black  What is ∼p? There are some cats which are not black.  Truth Tables o 2 number of = how many rows p q p∨q p∧q T T T T T F T F F T T F F F F F o if at least 1 is true, p∨q is true o both have to be true for p∧q to be true  ex. p∨∼q p q ∼q p∧∼q T T F T T F T T F T F F F F T T  ex. (∼p∧q)∨p p q ∼p ∼p∧q (∼p∧q)∨p T T F F T T F F F T F T t T T F F T F F  Truth tables with
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