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.

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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.

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