CSD101 Discrete Structures: Propositional Logic

A statement that is either true or false, but not both.

A propositional variable can have one of two values: true (T) or false (F).

The branch of logic that deals with propositions, using truth values and logical operators.

Propositions combined with logical operators (connectives) to form more complex propositions.

The area of logic that focuses on the validity and soundness of arguments.

Analyzing algorithms to ensure their correctness and efficiency.

Finding the most efficient approaches to solve problems like sorting and searching.

Designing secure systems and protocols using mathematical principles.

A logical operator that is true only if both propositions are true, otherwise it is false.

A logical operator that is true if at least one proposition is true, and false only if both propositions are false.

A logical operator that is true if exactly one proposition is true, and false if both propositions are true or both are false.

In the context of logic, 'p' and 'q' are commonly used to represent propositions, which are statements that can be either true or false.

The logical operator 'pq' represents the conjunction (AND) of propositions 'p' and 'q', meaning that both propositions must be true for the conjunction to be true.

A proposition that is the opposite of another proposition. It's created by adding 'not' or 'it is not the case that' to the original proposition.

A logical operator that combines two propositions using the word 'and'. The resulting proposition is true only if both original propositions are true.

A logical operator that combines two propositions using the word 'or'. The resulting proposition is true if at least one of the original propositions is true.

A logical operator that connects two propositions with the word 'if...then'. It states that if the first proposition is true, then the second proposition must also be true.

A logical operator that connects two propositions with the words 'if and only if'. It states that the two propositions are equivalent, meaning they have the same truth value.

A table that shows the truth value of a logical expression for all possible combinations of truth values for its propositional variables.

A logical operator that operates on a single proposition, changing its truth value.

Symbols or operators that connect propositions to create more complex logical statements. Examples include AND, OR, NOT, and IMPLICATION.

The ability to create and understand mathematical arguments, which often involve proving a statement or theorem. This skill is central to many areas of computer science.

A method for presenting a statement as true by a logical sequence of steps, each supported by previously established facts, definitions, or axioms.

The study of whole numbers and their properties, which involves concepts like divisibility, prime numbers, and modular arithmetic. It forms the foundation of many algorithms and data structures.

A systematic way of representing data using a set of elements and their relationships. It forms the basis for a wide range of applications, including databases, graphs, and algorithms.

Mathematical concepts that define the relationships between elements of sets. They are used in many areas of computer science, including relational databases and graph algorithms.

The converse of a conditional statement p → q is q → p. It essentially reverses the order of the hypothesis and conclusion.

The contrapositive of a conditional statement p → q is ¬q → ¬p. It negates both the hypothesis and the conclusion, and then switches their positions.

The inverse of a conditional statement p → q is ¬p → ¬q. It negates both the hypothesis and the conclusion, but doesn't reverse their positions.

A bi-conditional statement, denoted by p ↔ q, is true only when both p and q have the same truth value. It is equivalent to saying 'p if and only if q'.

In a bi-conditional statement p ↔ q, if p is true when q is true, and p is false when q is false, then the statement is true. It means the two parts are equivalent.

A logical operator representing 'and' in propositional logic. It evaluates to true only when both operands are true.

A logical operator representing 'or' in propositional logic. It evaluates to true when at least one operand is true.

A logical operator representing 'exclusive or' in propositional logic. It evaluates to true when only one operand is true.

A logical operator representing 'implication' in propositional logic. It evaluates to true unless the first operand is true and the second operand is false.

The statement in an implication that comes before the 'then'.

The statement in an implication that comes after the 'then'.