DISCRETE COMPUTATIONAL STRUCTURES
MODULE -1
LOGICAL CONNECTIVES AND TRUTH TABLES
❖ TRUTH TABLE
A truth table is a chart of rows and columns showing the truth value (either
“T” for True or “F” for False) of every possible combination of the given
statements (usually represented by uppercase letters P, Q, and R) as
operated by logical connectives.
➔ Two Components of a Truth Table
1.Statement : A statement is a sentence or mathematical
expression that is either definitely true or definitely false but not
both. It is usually denoted by an uppercase letter or variable.
The common ones are P, Q, R, and S.
2.Logical Connective: A logical connective is a word usually
written as a symbol that carries a particular instruction of logic
on how to operate a statement or compound statement. Logical
connectives can also be used to join or combine two or more
statements to form a new statement.
The Five Common Logical Connectives
1. Logical Negation
2. Logical Conjunction (AND)
3. Logical Disjunction (Inclusive OR)
4. Logical Implication (Conditional)
5. Logical Biconditional (Double Implication)
,I. Truth Table of Logical Negation
The negation of a statement is also a statement with a truth value that is
exactly opposite that of the original statement. For instance, the negation of
the statement is written symbolically as ~ or \neg ¬ is read as NOT.
II. Truth Table of Logical Conjunction
A conjunction is a type of compound statement that is comprised of two
propositions (also known as simple statements) joined by the AND
operator.The symbol that is used to represent the AND or logical conjunction
operator is \color{red}\Large{\wedge}∧. It looks like an inverted letter V.
, III. Truth Table of Logical Disjunction
A disjunction is a kind of compound statement that is composed of two
simple statements formed by joining the statements with the OR operator.
In a disjunction statement, the use of OR is inclusive. That means “one or
the other” or both.The symbol that is used to represent the OR or logical
disjunction operator is \color{red}\Large{ \vee }∨. It resembles the letter
V of the alphabet.
IV. Truth Table of Logical Implication
An implication (also known as a conditional statement) is a type of
compound statement that is formed by joining two simple statements with
the logical implication connective or operator.The symbol that is used to
represent the logical implication operator is an arrow pointing to the right,
thus a rightward arrow.
MODULE -1
LOGICAL CONNECTIVES AND TRUTH TABLES
❖ TRUTH TABLE
A truth table is a chart of rows and columns showing the truth value (either
“T” for True or “F” for False) of every possible combination of the given
statements (usually represented by uppercase letters P, Q, and R) as
operated by logical connectives.
➔ Two Components of a Truth Table
1.Statement : A statement is a sentence or mathematical
expression that is either definitely true or definitely false but not
both. It is usually denoted by an uppercase letter or variable.
The common ones are P, Q, R, and S.
2.Logical Connective: A logical connective is a word usually
written as a symbol that carries a particular instruction of logic
on how to operate a statement or compound statement. Logical
connectives can also be used to join or combine two or more
statements to form a new statement.
The Five Common Logical Connectives
1. Logical Negation
2. Logical Conjunction (AND)
3. Logical Disjunction (Inclusive OR)
4. Logical Implication (Conditional)
5. Logical Biconditional (Double Implication)
,I. Truth Table of Logical Negation
The negation of a statement is also a statement with a truth value that is
exactly opposite that of the original statement. For instance, the negation of
the statement is written symbolically as ~ or \neg ¬ is read as NOT.
II. Truth Table of Logical Conjunction
A conjunction is a type of compound statement that is comprised of two
propositions (also known as simple statements) joined by the AND
operator.The symbol that is used to represent the AND or logical conjunction
operator is \color{red}\Large{\wedge}∧. It looks like an inverted letter V.
, III. Truth Table of Logical Disjunction
A disjunction is a kind of compound statement that is composed of two
simple statements formed by joining the statements with the OR operator.
In a disjunction statement, the use of OR is inclusive. That means “one or
the other” or both.The symbol that is used to represent the OR or logical
disjunction operator is \color{red}\Large{ \vee }∨. It resembles the letter
V of the alphabet.
IV. Truth Table of Logical Implication
An implication (also known as a conditional statement) is a type of
compound statement that is formed by joining two simple statements with
the logical implication connective or operator.The symbol that is used to
represent the logical implication operator is an arrow pointing to the right,
thus a rightward arrow.
