Propositional Logic
Introduction to Logic
Logic defines a formal language for representing knowledge and for making logical inferences. It helps us to understand how to construct a valid argument.
Logic defines:
- Syntax of statements
- The meaning of statements
- The rules of logical inference (manipulation)
Propositional Logic
Definition: A proposition is a statement that is either true or false.
Examples:
- Dubai is the capital city of UAE. Answer: False.
- 3 + 4 = 7. Answer: True.
- How are you today? Answer:A question is not a proposition.
- x + y = 3 Answer: It is neither true nor false.
Composite Statements
More complex propositional statements can be build from elementary statements using logical connectives.
Examples:
- Proposition A: ″ It is sunny today″
- Proposition B: ″We will go to the park″
- A new (combined) proposition:″If it is sunny today then we will go to the park″
Logical connectives
- Negation
- Conjunction
- Disjunction
- Exclusive
- Implication
- Biconditional
Negation
Definition: Let p be a proposition. The statement ″It is not the case that p.″ is another proposition, called the negation of p. The negation of p is denoted by ¬p and read as "not p″.
Examples
- Pasadena is located in the State of California. The negation of this statement is:
It is not the casethat Pasadena is located in the State of California.
- 15 is not a prime number.
Exercise: Negate the following propositions:
- It is sunny outside. Answer: It is not sunny outside
- 3 is a prime number. Answer: 3 is not a prime number
- Spain is in Europe. Answer: Spain is not in Europe.
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Date of last modification: February 27, 2019