“Education is the most powerful weapon which you can use to change the world.” ― Nelson Mandela Do Now. Explain in your own words what deductive reasoning is. Exit Slip Error Analysis. Compare your exit slip to this one. Problem Solving at an early age. Deductive Reasoning II.
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Explain in your own words what deductive reasoning is.
Compare your exit slip to this one.
Deductive Reasoning II
Judging the validity of conditional statements
Explain the laws used in the deductive reasoning process.
Use deductive reasoning to lead to accurate conclusions.
Use the Law of Detachment
Use the Law of Syllogism
Use Problem Solving Skills
All quadrilaterals have four sides.
If it’s a quadrilateral, then it has four sides.
Inverse?
If it’s not a quadrilateral, then it does not have four sides.
In other words, it has more or less than four sides.
A triangle has, at most, one right angle.
If it’s a triangle, then it has, at most, one right angle.
Inverse?
If it’s not a triangle, then it has more than one right angle.
Two lines in a plane always intersect at exactly one point
If there are two lines in a plane, they intersect at exactly one point
Negation?
If there are two lines in a plane, they do not intersect at exactly one point.
In other words, they do not intersect at all or they intersect at more than one point.
Counterexample: Parallel lines!
Axiom – a self-evident truth that requires no proof; a statement accepted as fact
Postulate – a proposition that requires no proof
Theorem – a proposition that can be deduced from the premises or assumptions of a system
Corollary – a proposition that is incidentally proved in proving another proposition
Reflexive Property
Symmetric Property
Transitive Property
A=A
A quantity is equal to itself
In logic, A A.
Always true in logic
If you’re a student at Simon Tech, then you’re a student at Simon Tech.
If a pentagon has five sides, then a pentagon has five sides.
If A=B then B=A
Always true of numbers (if x=5 then 5=x)
In logic, If A B, then B A.
Not always true.
If I eat too much I get sick. If I get sick then I eat too much.
But when is it true?
When the Biconditional statement is true.
For example, “Two lines intersect iff they are not parallel”
Transitive Property
Christian wrote the following argument:
If the soccer team loses, Janalee won’t watch their next game.
Janalee watched their next game.
Therefore, the soccer team lost.
No. But what can Christian conclude?
The soccer team won.
Jessica wrote the following argument:
If the sun is out, then Karina will go to the beach.
If she does not go with friends, then Karina will not go to the beach.
The sun is out.
Therefore, Karina goes with friends.
Any time you use logical evidence, you are using deductive reasoning!
Inductive or Deductive?
Inductive
Inductive or Deductive?
Deductive
Inductive or Deductive?
Deductive
W
True
Therefore, it will not start.
Invalid.
A, B, and C could all lie in plane G and still be collinear.
Valid.
Uses the Law of Detachment.
W
Therefore, If you get a job, then you will buy a car.
W
B
Law of Syllogism (Transitive Property)
W
Therefore, school will be closed.
Law of Detachment
W
Therefore MA = MB.
Law of Syllogism.
W
Explain the laws used in the deductive reasoning process.
Use deductive reasoning to lead to accurate conclusions.
Use the Law of Detachment
Use the Law of Syllogism
Use Problem Solving Skills
For #1, fill in both blanks and explain your reasoning.