Logical Operators in Brief with examples

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  • 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