15 Slides--Conditionals

15 Slides--Conditionals - CS103A HO#15 Slides-Conditionals...

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CS103A HO#15 Slides--Conditionals 1/28/08 1 Conditionals P Q P ? Q T T T T F F F T T F F T Conditionals P Q P ? Q T T T T F F F T T F F T Observation 1: The ? connective is pretty weak. Knowing that P ? Q is true only eliminates one possible combination of P and Q. Observation 2: If we know P ? Q is true and we also know P is false, then we have no information about the truth of Q. Observation 3: If we know P ? Q is true and we also know P is true, then we are sure Q is true. Conditionals P Q P ? Q ¬P Q T T T T T F F F F T T T F F T T Conditionals P Q P Q ¬P Q T T T T T F F F F T T T F F T T is called the material conditional , meaning that it is truth-functional Conditionals P Q P Q ¬P Q T T T T T F F F F T T T F F T T The best rendering of P Q in English is " if P, then Q " Antecedent Consequent P Q P Q ¬P Q T T T T T F F F F T T T F F T T \$40K New Copier \$40K New Copier Is this true: If the department gets an extra \$40K, we'll buy a new copier.

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CS103A HO#15 Slides--Conditionals 1/28/08 2 P Q P Q ¬P Q T T T T T F F F F T T T F F T T If the moon is not made of cheese, then triangles have three sides.
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15 Slides--Conditionals - CS103A HO#15 Slides-Conditionals...

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