Truth Functions

Truth Functions

Truth Functions

Addition

Truth Functions

• It's raining and the game is over.

p & q

 

• The symbol & ("and") is like a function that takes two sentences ("p" and "q") as inputs.

Truth Functions

p: Squares have four sides.

q: Snow is white.

r: Fish have four legs.

s: Triangles are round.

 

1. Squares have four sides and fish have four legs.
   p & r
    
2. Squares have four sides and snow is white.
   p & q
    
3. Fish have four legs and triangles are round.
   r & s
    

Truth Functions

Possible cases:

1. INPUT: One true, one false. OUTPUT: false.
2. INPUT: Both true. OUTPUT: true.
3. INPUT: Both false. OUTPUT: false.

 

1. Squares have four sides and fish have four legs.
   p & r
    
2. Squares have four sides and snow is white.
   p & q
    
3. Fish have four legs and triangles are round.
   r & s
    

Truth Functions

Possible cases:

1. INPUT: One true, one false. OUTPUT: false.
2. INPUT: Both true. OUTPUT: true.
3. INPUT: Both false. OUTPUT: false.

 

 

p = TRUE; q = FALSE; r = TRUE; s = FALSE

 

1. p & q

2. q & s

3. s & r

4. r & (p & q)

 

Truth Functions

Key Concepts

• Truth Functions
  AKA: Logical operator / logical connective / sentential connective / truth-functional operator