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

T FF T

p: I live in Honolulu~p: I do not live in Honolulu

Truth Table: Conjunction

p q p ˄ qT T TT F FF T FF F F

1. 3 + 2 = 5 and London in in England.2. 3 + 2 = 5 and London is in France.3. 3 + 2 = 6 and London is in England.4. 3 + 2 = 6 and London is in France.

Truth Table: Disjunction

p q p V qT T TT F TF T TF F F

1. 3 + 2 = 5 and London is in England.2. 3 + 2 = 5 and London is in France.3. 3 + 2 = 6 and London is in England.4. 3 + 2 = 6 and London is in France.

Constructing Truth Table

• Construction a truth table for:~(p ˄ q)

p q p ˄ q ~(p ˄ q)T T T FT F F TF T F TF F F T

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)

p q p V q ~(p V q)T T T FT F T FF T T FF F F T

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?)