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CSCI-C 241 Notes

P T T F F

Q T F T F

P∧Q T F F F

Logic Gates P∨Q P⊕Q T F T T T T T F

P∧Q – P and Q P∨Q – P or Q  Either P or Q  P⊕Q – P XOR Q In English:  P or Q, but only one.  One and only one of P or Q P→Q – If P then Q In English:  While P, Q.  If P, Q.  If P, then Q.  When P, Q.  Provided that P, Q  In the case that P, Q  Where P, Q. Conclusion tags:  P, only if Q  Only if Q will P be true  P, only when Q  Q is a necessary condition for P ---------------------“The TV is on if and only if it is plugged in” – No on/off switch “The fridge is on if and only if it is plugged in” – makes sense (PQ) ∧ (QP) “Bi-implication” or “Biconditional” “If and only if” “When and only when” “P is a necessary and sufficient condition for Q”

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P→Q T F T T

P↔Q T F F T

¬P F F T T

Negation ¬P Means that it is not true that P If P = “Everyone in this room is a student ¬P =   

Not everyone in this room is a student It is not true that everyone in this room is a student Someone in this room is not a student

Ambiguous:  Everyone in this room is not a student

These are not translations for ¬P:  Everyone not in this room is a student  No one in this room is a student...