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We know that the simple statements are represented as p, q and so on. Suppose we are given a compound preposition.

There is another property of compound prepositions called the **duality**; Therefore, the dual of above statement is

The dual can be achieved by interchanging by or interchanging by . This means and is dual of each other.

### Dual For Another Type Of Statement

We will see an example of another type of prepositional statement in which we use True or False directly instead of a variable.

For example,

```
is a preposition with T or True as one of the variable.
```

The dual of such a statement can be obtained by interchanging by and interchanging **True **with **False** or **False **with **True**.

Each of the statement can be derived from the other.

### Understanding Duality Using Truth Tables

These are the truth tables for the statements – and .

T | T | T |

T | F | F |

F | T | F |

F | F | F |

T | T | T |

T | F | T |

F | T | T |

F | F | F |

If we change the operator for with , or vice-versa, we get dual of each other. The truth table validates this claim. We can check this for other prepositional statements also.