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3.1.1 Types of Proposition
A proposition is of two types, which are as follows:
• Simple proposition: It contains a single atomic statement. Some examples of simple propositions are:
1. “Java is an object-oriented programming language.”
2. “The earth revolves around the sun.”

• Compound proposition: It contains two or more simple propositions joined by special symbols called
connectives.
Some examples of compound propositions are:
1. “Java is an object-oriented programming language and Java is platform-independent.”
2. “He is playing the piano or he is playing the flute.”
In the first example, the connective “and” is used and the connective “or” is used in the second example.

3.2 WELL-FORMED FORMULAS AND TRUTH VALUES
Well-Formed Formulas (WFF) are the representation of propositional logic in the form of symbols or abbreviations. It
is a statement that can either be true or false. Thus, all simple propositions are well-formed formulas. For example,
A: Java is an object-oriented programming language.

B: Java is platform-independent.
In the above example, both statements are represented by symbols, i.e., A and B. Hence, it is a well-formed formula.
Any propositional statement formed by using A and B, then (A ∧ B), (A ∨ B), (A → B), etc. are well-formed formulas.

3.2.1 Truth Value and Truth Table
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.
A compound proposition is truth-functional, which means it accepts truth values as input and produces a unique
truth value as output.
The logical process of finding conclusions from given propositions is known as syllogism and the propositions used to
draw conclusions are called the premises.
A proposition is generally expressed and evaluated with the help of a truth table. The truth table is a table containing
all possible combinations of inputs and their corresponding outputs listed in tabular form. Truth values in a truth
table are denoted either by T and F or by 1 and 0. A logic circuit’s truth table with n binary inputs will have 2ⁿ input
combinations or rows. For example, the truth table of disjunction is given below:

a b a ∨ b
0 0 0

0 1 1
1 0 1
1 1 1

Definition
A truth table is a table which shows the truth values of all the possible combinations of inputs. It is used to find if a
compound statement is true or false.

68 Touchpad Computer Science (Ver. 3.0)-XI