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1.1 PROPOSITIONAL LOGIC
Propositional Logic is a branch of symbolic logic that deals with propositions and how each proposition relates to
others. It studies the ways of joining or changing propositions to form more complex propositions. A proposition is
represented by proposition variables containing a single alphabet generally written in lower case.
Definition
A proposition is a declarative statement which can either be true or false, but not both or any other value.
A proposition can be of two types:
• Simple proposition: It contains a single atomic statement. Some examples of simple propositions are as follows:
“Python is the best programming language used in artificial intelligence”.
“Planet Mars is named after the Roman God of war”.
• Compound proposition: It contains two or more simple propositions joined by special symbols called connectives.
Some examples of compound propositions are as follows:
“Mercury is the smallest planet in the solar system and it has no moon”.
“Raj is playing online games or he is playing football in the field”.
In the first example connective “and” is used, and “or” is used in the second example.
1.2 TRUTH VALUES
The truth or falsity of a proposition is called its Truth Value. A simple proposition can either be true or false. The truth
value of a compound proposition is calculated from the truth values of its components using certain logical rules.
Compound propositions are truth-functional which means they accept the truth values as input and produce a unique
truth value as output.
Definition
A table containing all the possible combinations of inputs and their corresponding outputs listed in the tabular form
is called a truth table. The truth values in a truth table are denoted either by T and F or by 0 and 1. A truth table with
n binary inputs will have 2ⁿ input combinations or rows.
There are two methods to draw a conclusion. They are:
• Algebraic method
• Truth table method
A proposition is generally expressed and evaluated with the help of a truth table.
The constants 0 representing false and 1 representing true are called logical constants or Boolean constants.
The variables which store logical constants are called binary-valued quantities or logical variables or Boolean
variables.
Truth tables can be used to deduce the logical expression for a given digital circuit.
1414 Touchpad Computer Science-XII

