Introducing the truth table

We can also describe the conjunction operation in what we call a truth table. In the table, each column represents a proposition or a compound proposition.

In the table below, the first two columns (labelled (p) and (q)) represent two propositions (or propositional variables) and the rows represent all possible combinations of how you can assign the values true and false to the variables (p) and (q).

The final column labelled (p land q) is a compound proposition. The value of the compound proposition is dependent on the variable (p) and (q). The value of each row is the result of the compound statement when (p) and (q) have the values indicated in the same row.

(p)	(q)	(p land q)
(F)	(F)	(F)
(F)	(T)	(F)
(T)	(F)	(F)
(T)	(T)	(T)

This representation of a compound proposition (a truth table) will be used a lot in this course, and we will look at how to fill in truth tables for more complicated logical statements later.

It is important that you know the truth table for conjunction and you should be able to recall it.

In the next activity, we will look at the disjunction operator and how it differs from conjunction.