Download 2.3 Apply Deductive Reasoning

2.3 Apply Deductive Reasoning
inductive reasoning drawing conclusions based on observations and
patterns
deductive reasoning using facts, definitions, accepted properties, and
logic to form a formal argument
Laws of Logic
Law of Detachment
If a hypothesis of a conditional statement is true, then
the conclusion is also true.
ex: Mrs. Carpenter goes to the football games every
Thursday.
It is Thursday.
Therefore Mrs. Carpenter is going to the football
game.
Law of Syllogism If these statements are both true, . . .
If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
then this statement is true.
If hypothesis p, then conclusion r.
ex. If Amanda does her chores, she gets an
allowance.
If Amanda gets an allowance, she will buy an
iPhone.
If Amanda does her chores, she will buy an
iPhone.
You try:
Use the Law of Detachment to make a valid conclusion in each
situation below · I have three cents in my pocket. The only way to make three
cents is with three pennies. . .
Therefore, I have three pennies.
o
o
o
· If 0 < m<K < 90 , then <K is an acute angle. <K is 38 . . .
Therefore, <K is an acute angle.
o
· If two angles have a sum of 90 , then they are complementary
o
o
angles. m<A = 36 and the m<B = 54 . . .
Therefore <A and <B are complementary angles.
· Every Friday and Saturday Mrs. Burwell goes shopping.
Today is Tuesday . . .
Therefore Mrs.Burwell is not shopping.
You try:
Use the Law of Syllogism to make a valid conclusion in each
situation below o
· If the measure of an angle is 90 , then it is a right angle.
If an angle is a right angle, then the lines forming the angle are
perpendicular.
Therefore . . .
o
If the measure of an angle is 90 , then the lines forming the angle
are perpendicular.
o
o
· If 0 < m<K < 90 , then <K is an acute angle.
o
o
o.
If m<K is 38 , then 0 < m<K < 90
Therefore. . .
o
If m <K is 38 , then <K is an acute angle.
Draw some conclusions:
Use inductive reasoning to make conjectures. Then use deductive
reasoning to show the conjecture is true.
What conclusions can you make about . . .
· the product of two odd integers
·
the sum of two odd integers
·
the product of zero and any other real number
FYI:
http://www.classzone.com/cz/books/geometry_2007_na/resources/applications/animations/2_
3.html
p90:1, 4, 6, 7-13all, 16, 21, 24, 25-27all