Mathematical Logic Basics

[khaled]

Here are the most basic Logic Operations:

 

AND ([math]\wedge[/math]): The intersection of two statements, [math]A \wedge B[/math] is TRUE when A is TRUE and B is TRUE

 

Example: "It's dark blue" = "It is dark [math]\wedge[/math] It is blue"

 

OR ([math]\vee[/math]): The union of two statements, [math]A \vee B[/math] is TRUE when A is TRUE or B is TRUE, or both

 

Example: "Xittenn drinks tea or coffee" = "Xittenn drinks tea [math]\vee[/math] Xittenn drinks coffee"

 

NOT (¬): The negation operator, ¬A is TRUE when A is FALSE

 

Example: "I am not a liar" = "¬ I am liar"

 

Implication ([math]\longrightarrow[/math]): One statement enforce another, [math]A \rightarrow B[/math]

 

Example: "A locked door cannot be opened" = "The door is locked \longrightarrow The door cannot be opened"

 

Equivalence ([math]\Leftrightarrow[/math]): Two statements are equivalent, [math]A \Leftrightarrow B[/math]

 

Example: "Jon and Monica go out together, or don't" = "Jon goes out [math]\Leftrightarrow[/math] Monica goes out"

 

Here is a truth table for more operations, which are easy to understand with the Venn diagram:

 

Edited April 13, 2012 by khaled