Logical Operators in Brief with examples
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This document defines and explains different types of logical operators: negation, conjunctions, disjunctions, conditionals, and bi-conditionals. It provides examples of each operator and includes their truth tables showing how the operators evaluate statements as true or false based on the truth values of the individual statements.
Logical Operators in Brief with examples
- 1. Types of Argument (Logical operators) By:Mujtaba Khan
- 2. Logical Operators • In logic, a logical operators (also called a logical connectives) is a symbol or word used to connect two or more sentences in a grammatically valid way.
- 3. Types of logical Operators • Negation • Conjunctions • Disjunctions • Conditional • Bi-conditional
- 4. Negation • Changing a statement so that it has the opposite meaning and truth values • Also known as “Not” • The symbol for negation is ‘~’ • Example: P: There is snow on the ground ~P: There is not snow on the ground
- 5. Truth Table for Negation P T F ~P F T
- 6. Conjunctions • A proposition that presents two or more alternative terms, with the assertion that both are true. • Also known as And. • symbol that we use is ‘^’ (Looks like an A without the middle line – ). • Example: – P: I found $5 – Q: I crashed my car into a telephone pole – P^Q: I found $5 AND I crashed my car into a telephone pole.
- 7. Truth Table for “And” • A conjunction is only true if all of the statements in it are true, otherwise it is false P Q P^Q T T T T F F F T F F F F
- 8. Disjunctions • A proposition that presents two or more alternative terms, with the assertion that at least one is true. • Also known as “Or” • symbol that we use is ‘V’ • Example: – P: The number 3 is odd – Q: 57 is a prime number – PVQ: The number 3 is odd OR 57 is a prime number.
- 9. Truth Table for “Or” • A disjunction is true if at least one of the statements in it are true, otherwise it is false. P Q PVQ T T T T F T F T T F F F
- 10. Conditionals • An conditional is only false when the first statement is true and the second one is false, otherwise it is true. • Also known as an “If-Then” Statement • An Conditional for statements P and Q is denoted P=> Q • An Conditional is read either “If P, then Q” or “P implies Q” • Example: If you brush every day, you probably won’t get cavities or gum disease.
- 11. Truth Table for “If-Then” • An conditional is only false when the first statement is true and the second one is false, otherwise it is true. P Q P=>Q T T T T F F F T T F F T
- 12. Bi-conditional • Bi-conditionals are true when both statements have the exact same truth value. • Also known as “ If and only If ” • An Biconditional for statement P and Q is denoted by P<=> Q • An Bi-conditional is read “P if and only if Q” • Example: The candidate becomes president if and only if he wins the election
- 13. Truth Tables for Biconditional P Q P<=>Q T T T T F F F T F F F T A Bi-conditional is only true when the truth values of ‘P’ and ‘Q’ are the same
- 14. THANK YOU