Logical Operators

Logical Operators

1. Negation ~ / ¬ / not

   • p = Michael’s PC runs Linux
     • ¬p = Michael’s PC does not runs Linux

2. Conjunction ^ / and

   • p = “Rebecca’s PC has more than 16 GB free hard disk space,
     • q = "Rebecca’s PC runs faster than 1 GHz."
       • p ^ q = “Rebecca’s PC has less than 16 GB free hard disk space, and its processor does not run faster than 1 GHz"

3. Disjunction v / or

   • p = 12 is divisible by 3
     • q = 3 is a prime number.
       • p V q = 12 is divisible by 3 or 3 is a prime number

4. Exclusive OR ⊕

   • proposition that is true when exactly one of p and q is true and is false otherwise
     • Students who have taken calculus or computer science, but not both, can enroll in this class.

5. Conditional → / implies

   • p - "Maria learns computer science"
     • q = “Maria will find a good job."
       • p → q = "If Maria learns computer science, then she will find a good job"

6. Bi-conditional ↔

   • ? ↔ ? is true when p and q have the same truth values, and is false otherwise
     • p = "You can take the flight"
       • q = "You buy a ticket"
         • p ↔ q = You can take the flight if and only if you buy a ticket.”

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