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.
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.
It was windy, or it did not rain and it was not cold.
It was not windy and it was cold.
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
p q ∼q p∧∼q
T T F T
T F T T
F T F F
F F T T
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