# Prepositional Logic – Simple Statements

Prepositional Logic is kind of logic that studies “Statements” and derives relationship among those statements.

#### What is a statement or a preposition ?

When we talk we make many sentences but all sentences are not ‘Statements”. A sentence qualify as a statement when it has a truth value. There is only two truth value for a statement – true or false.

For example,

`What is your name ?`

The above sentence is a question and we cannot give a truth value for this sentence. It is neither true nor false.

If someone reply to the question with an answer such as following

`My name is Peter.`

The above is an example of statement because it can be true or false.

### Simple Preposition and Compound Preposition

Suppose there are two prepositions.

```I am eating.
I am sleeping.```

Such individual statement are called simple prepositions and we do not need to write them every time. Instead we can assign an alphabet to each of these statements.

```p : I am eating.
q:  I am sleeping.```

We can also make complex statements using these simple prepositions. However, we need a logical connective to do that.

There are many logical connectives but the most common connectives are

```and  ( conjunction )
or   ( disjunction )```
`p ∧ q  and p ∨ q  are compound statements.`

It means following

```p ∧ q : I am eating and I am sleeping.
p ∨ q : I am eating or I am sleeping.```

The truth value of the compound preposition depends on the individual simple preposition in the compound preposition.

In the above example, suppose truth value of p is true and q is false, then

= p ∧ q

= true ∧ false

= false

Similarly,

=p ∨ q

= true ∨ false

= true

We shall see more of these using a truth table in future lessons.