Mathematical Logic Basics

[khaled]

Here are the most basic Logic Operations:

 

AND ($\wedge$): The intersection of two statements, $A \wedge B$ is TRUE when A is TRUE and B is TRUE

 

Example: "It's dark blue" = "It is dark $\wedge$ It is blue"

 

OR ($\vee$): The union of two statements, $A \vee B$ is TRUE when A is TRUE or B is TRUE, or both

 

Example: "Xittenn drinks tea or coffee" = "Xittenn drinks tea $\vee$ Xittenn drinks coffee"

 

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

 

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

 

Implication ($\longrightarrow$): One statement enforce another, $A \rightarrow B$

 

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

 

Equivalence ($\Leftrightarrow$): Two statements are equivalent, $A \Leftrightarrow B$

 

Example: "Jon and Monica go out together, or don't" = "Jon goes out $\Leftrightarrow$ 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