TRUTH TABLE
TRUTH TABLE is A convenient method for analyzing a compound statement is to make a truth table for it.
A truth table specifies the truth value of a compound proposition for all possible truth values of its constituent propositions.
The truth values “true” and “false” are respectively denoted by the letters T and F.
Truth Table:
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:
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.
TRUTH TABLE is A convenient method for analyzing a compound statement is to make a truth table for it.
A truth table specifies the truth value of a compound proposition for all possible truth values of its constituent propositions.
The truth values “true” and “false” are respectively denoted by the letters T and F.
Truth Table:
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: | 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.
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