4 - LECTURE 4: MORE LOGIC (2.5-2.8) All truths are easy to...

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LECTURE 4: MORE LOGIC ( § 2.5-2.8) All truths are easy to understand once they are discovered; the point is to discover them. Galileo Galilei (1564 - 1642) 1. More terminology for implications Let P and Q be statements. Recall that P Q has the following truth table: P Q P Q T T T T F F F T T F F T We can read this in many ways: “If P (is true) then Q (is true).” “ P implies Q .” “ Q if P .” “ P only if Q .” “ P is sufficient for Q .” “ Q is sufficient for P .” We call P the premise and Q the conclusion of the implication P Q . What if we switch the premise and conclusion and form the new statement Q P ? Is this the same thing? No! Try the following example: “If it rains on me then I get wet.” This is true, but if we switch the premise and conclusion we get “If I get wet then it rains on me.” which is false. When we switch the premise and conclusion, and form Q P we call this the converse of P Q . What happens with (
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This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.

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4 - LECTURE 4: MORE LOGIC (2.5-2.8) All truths are easy to...

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