Truth Tables

A truth table is a table that shows how a Boolean expression's value can be computed. The procedure in constructing a truth table is to first add a column to the table for each variable involved in the expression. Then we compute the value of each sub-expression of the expression in its own column until we have computed the entire expression in the final column.

There are four logical operators that we will be working with
  • The negation operator (¬P), which returns true if the variable P is false, and returns false otherwise.
  • the or operator (P ∨ Q), which returns true if P is true or Q is true, or if both are true, and returns false otherwise.
  • the and operator (P ∧ Q), which returns true if both P and Q are true, and returns false otherwise.
  • the implies operator (P → Q), which returns false if P is true and Q is false, and returns true otherwise.

Learning about Truth Tables