Propositional Logic
Truth Table
Subjects to be Learned
Contents
Often we want to discuss properties/relations common to all propositions.
In such a case
rather than stating them for each individual proposition we use variables representing
an arbitrary proposition and state properties/relations in terms of those variables.
Those variables are called a propositional variable.
Propositional variables are also considered a proposition and called a proposition
since they represent a proposition
hence they behave the same way as propositions.
A proposition in general contains a number of variables. For example
(P Q) contains variables P and Q each of which
represents an arbitrary proposition. Thus a proposition takes different values
depending on the values
of the constituent variables. This relationship of the value of a proposition and those
of its constituent variables can be represented by a table. It tabulates the value
of a proposition for all possible values of its variables and it is called a
truth table.
For example the following table shows the relationship between the values of P, Q
and P Q:
OR
P | Q | (P Q) |
F | F | F |
F | T | T |
T | F | T |
T | T | T |
In the table, F represents truth value false and T true.
This table shows that P Q is false
if P and Q are both false, and it is true in all the other cases.
Test Your Understanding of Truth Table
Which of the following tables are a truth table ?
Z below represents a proposition involving P and Q.
Table 1
P | Q | Proposition Z |
F | F | F |
T | F | T |
T | T | T |
T | F | T |
Table 2
P | Q | Proposition Z |
F | F | F |
T | F | T |
T | T | F |
Table 3
P | Q | Proposition Z |
F | F | F |
F | T | T |
T | F | T |
T | T | T |
Table 4
P | Proposition Z |
F | F |
F | T |
T | F |
For each of the above tables, click "Yes" if it is a truth table, else click "No" below,
then click Submit.
Next -- Connectives
Back to Schedule
Back to Table of Contents