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 **

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