1. Section 2.3: Deductive Reasoning
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2. Goals Use symbolic notation to represent logical statements
Form conclusions by applying the laws of logic to true statements
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3. Symbolic Notation` Conditional Statement Converse Inverse
p → q
Converse
q → p
Inverse
~p → ~q
Contrapositive
~q → ~p
Biconditional
p  q
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4. Example 1: Using Symbolic Notation
Let p be “the value of x is -4” and q be “the square of x is 16.”
Write p → q in words
If the value of x is -4, then the square of x is 16
Write q → p in words
If the square of x is 16, then the value of x is -4
Decide whether the biconditional statement p  q is true
the conditional statement in part (a) is true, but the converse in part (b) is false
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5. Example 2: Writing an Inverse and a Contrapositive
Let p be “today is Monday” and q be “there is school.”
a) Write the contrapositive of p → q.
~q → ~p, if there is no school, then today is not Monday
b) Write the inverse of p → q
~p → ~q, If today is not Monday, then there is no school
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6. Using The Laws of Logic Inductive Reasoning Deductive Reasoning
Looking at several specific situations to arrive at a conjecture
Deductive Reasoning
Uses a rule to make a conjecture
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7. Laws of Deductive Reasoning
Logical Argument
Using facts, definitions, and accepted properties in a logical order
Laws of Deductive Reasoning
Law of Detachment
Law of Syllogism
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8. Law of Detachment
If p → q is a true statement and p is true, then q is true
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9. Law of Syllogism
If p → q and q → r are true conditionals, then p → r is also true
Geometry
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