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 
. A sentence qualifies as a statement when it has a truth value. There is only two truth value for a statement – 
or 
.
For example,
What \hspace{5px}is \hspace{5px}your \hspace{5px}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 \hspace{5px}name \hspace{5px} is \hspace{5px} 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.
\begin{aligned}
&I \hspace{5px}am \hspace{5px} eating.\\
&I \hspace{5px}am \hspace{5px} sleeping.
\end{aligned}Such individual statement is called simple prepositions and we do not need to write them every time. Instead, we can assign an alphabet to each of these statements.
\begin{aligned}
&p : I \hspace{5px} am \hspace{5px} eating.\\
&q: I\hspace{5px} am\hspace{5px} sleeping.
\end{aligned}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
\begin{aligned}
&and \hspace{5px} ( conjunction )\\
&or \hspace{5px} ( disjunction )
\end{aligned}and
are compound statements.
It means following
\begin{aligned}
&p \wedge q : I \hspace{5px} am \hspace{5px} eating \hspace{5px}and \hspace{5px}I \hspace{5px}am \hspace{5px}sleeping.\\
&p \vee q : I \hspace{5px}am \hspace{5px}eating \hspace{5px}or \hspace{5px}I \hspace{5px}am \hspace{5px}sleeping.
\end{aligned}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
\begin{aligned}
p \wedge q = true \wedge false = false
\end{aligned}Similarly,
\begin{aligned}
p \vee q = true \vee false = true
\end{aligned}We shall see more of these using a truth table in future lessons.
