Chapter 2.3 Notes: Apply
Deductive Reasoning
Goal: You will use deductive reasoning to form a logical argument.
Review of Conditional
Statements
Conditional:
Converse:
Inverse:
Contrapositive:
Write into foldable
Law of Detachment:
If the hypothesis is TRUE in the cond.
statement, then the conclusion is also TRUE
Law of Syllogism:
If p q, qr (new conclusion),
then pr
Deductive Reasoning
Deductive reasoning uses facts, definitions,
accepted properties, and the laws of logic to
form a logical argument.
This is different from inductive reasoning,
which uses specific examples and patterns to
form a conjecture.
Look @ your notes
Laws of Logic:
Use the Law of Detachment to make a valid conclusion in the true
situation.
Ex 1: Assuming that the following statements are true, “If Tim studies,
then he passes” and “Tim studies”, what conclusion can you make?
Ex 2: Assuming that the following statements are true, “If 2 lines are
parallel, then they never meet” and “AB and CD are parallel”, what
conclusion can you make?
Look @ your notes
The angle is acute
invalid
Look @ your notes
If Jack goes to the mall, then Pam will go to
If a # is a multiple of 54, then it is a multiple
Look @ your notes
If 2 angles are vertical, then their
measures are equal.
Ex.4: If possible, use the Law of Syllogism to write a new conditional
statement that follows from the pair of true statements.
a. If the radius of a circle is 4 ft, then the diameter is 8 ft. If the radius
of a circle is 4 ft, then its area is 16π ft2.
If the diameter is 8ft, then the area of the circle
is 16π ft2
.b. If Joe takes Geometry this year, then he will take Algebra 2 next
year. If Joe takes Algebra 2 next year, then he will graduate.
If Joe takes Geometry this year, then he will
graduate.
c. If y3 = 8, then y = 2. If y = 2, then 3y + 4 = 10.
If y3 = 8, then 3y + 4 = 10.