3.3: Truth Tables. Types of Statements Negation: ~p Conjunction: p ˄ q (p and q) Disjunction: p V q (p or q, or both) Conditional: p → q (if p, then q)

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3.3: Truth Tables

Types of Statements Negation: ~p Conjunction: p ˄ q (p and q) Disjunction: p V q (p or q, or both) Conditional: p → q (if p, then q) When are these statements true, or false?

Truth Table: Negation p~p TF FT p: I live in Honolulu ~p: I do not live in Honolulu

Truth Table: Conjunction pqp ˄ q TTT TFF FTF FFF = 5 and London in in England = 5 and London is in France = 6 and London is in England = 6 and London is in France.

Truth Table: Disjunction pqp V q TTT TFT FTT FFF = 5 and London is in England = 5 and London is in France = 6 and London is in England = 6 and London is in France.

Constructing Truth Table Construction a truth table for: ~(p ˄ q) pqp ˄ q~(p ˄ q) TTTF TFFT FTFT FFFT p: Harvard is a university. q: Yale is a university. ~(p ˄ q): It is not true that Harvard and Yale are universities. (true or false?)

Constructing Truth Table Construction a truth table for: ~(p V q) pqp V q~(p V q) TTTF TFTF FTTF FFFT p: Oahu is an island. q: Ripe mango is hard. ~(p V q): It is not true that Oahu is an island or that ripe mango is hard. (true or false?)