Deductive

1
Section 2.3

• Deductive
• Reasoning

2
Deductive Reasoning

• Deductive Reasoning is logical reasoning from
  given statements to a conclusion.
• If the given statements are true then deductive
  reasoning will produce a true conclusion.

3
Law of Detachment

• If p q is a true statement and p is true,
  then q must be true.
• A gardener knows that if it rains, the garden
  will be watered. It is raining. What conclusion
  can be made?
• The garden will be watered.

4
Law of Syllogism

• If p q and q r are true statements,
  then p r is a true statement.
• If a quadrilateral is a square, then it contains
  four right angles. If a quadrilateral contains
  four right angles, then it is a rectangle.
• What conclusion can be made?
• If a quadrilateral is a square, then it is a
  rectangle.

5
Check Understanding

• Use either the law of detachment or syllogism to
  draw a conclusion.

• If it rains, then Jan stays inside.
• If Jan stays inside, then she does not get wet.

• If it rains, then Jan does not get wet.
  (syllogism)

6
Check Understanding

• Use either the law of detachment or syllogism to
  draw a conclusion.
• If you make a field goal, then you score 3
  points.
• The Packers made a field goal.
• The Packers scored 3 points. (detachment)

7
Checking Understanding

• Use either the law of detachment or syllogism to
  draw a conclusion.
• If I lay out, then I will get tan.
• If it is sunny, I will lay out.
• If it is sunny, then I will get tan. (syllogism)

8
Checking Understanding

• Use either the law of detachment or syllogism to
  draw a conclusion.
• If I eat my veggies, then I will be healthy.
• I am healthy.
• Not possible.

9
Checking Understanding

• Use either the law of detachment or syllogism to
  draw a conclusion.
• If I am sad, then I eat chocolate.
• If I eat chocolate, then I will be happy.
• I am sad.
• I will be happy. (Law of syllogism and
  detachment)

10
Homework

• Page 84 87
• Problems2-20even, 28, 30, 34, 35