Inductive Reasoning
What is inductive reasoning?
Reasoning based off past events or patterns.
What is the hypothesis of the following statement:
I like apples if it is in a pie.
It is in a pie.
What is deductive reasoning?
Reasoning based off facts, either given or known.
If <1 and <2 are Vertical angles, what can be said about the two angles?
They are congruent.
Is the inverse of the statement True or False?
If it is sunny, then it is summer.
Inverse:
If it is not sunny, then it is not summer.
False (there could be a sunny day in the Spring).
What is the next expected number?
1, 4, 9, 16
25
Write a conditional for the following statement:
I like apples if it is in a pie.
If it is in a pie, then I like apples.
What is the Law of Detachment?
If p-->q and p is true, then q is true.
What reason could you use for the statement:
2x = 18
Division POE
Divide both sides by 2 to solve for x.
True or False:
When two lines intersect, they form linear pairs.
True.
What is next in this pattern?
0.5, 2, 4.5, 8, 12.5
18
What is a counterexample to the following conditional:
If x^2 = 9, then x is positive 3.
Counter: x = -3
What is the Law of Syllogism?
If p--> q and q-->r is true, then p-->r.
<1 and <2 are linear pairs and <1 = (72 + x) and <2 = (48), write a two-column proof to show the value of x.
72 + x + 48 = 180 Linear Pairs Theorem
120 + x = 180 Combine Like Terms
x = 60 Subtraction POE
True or False:
Angles whose sum is equal to 180 degrees are called complementary angles.
False.
What is a statement that is created from inductive reasoning but is not proven?
Conjecture.
Write the converse of the following statement:
If the weather is inconsistent, then you live in Iowa.
If you live in Iowa, then the weather is inconsistent.
What can you logically deduce using the Law of Detachment?
If Lin gets 92 or more on his next test, then he will get in A in the class.
Lin got a 94.
If p--> q and p is true, then q is true.
p--> q is true.
94 >92 --> so p is true.
Therefore, q is true. Lin got an A in the class.
<1 and <2 are congruent angles.
<1 and <3 are vertical angles.
<4 is a right angle.
<2 and <4 are supplementary angles.
What can you say about <3?
<3 is 90 degrees, or a right angle.
True or False:
Angles whose sum is equal to 90 degrees are called supplementary angles.
False.
How you show a conjecture is false?
Counterexample.
Identify the biconditional of the statement:
If the weather is inconsistent, then you live in Iowa.
The weather is inconsistent if and only if you live in Iowa.
What can you logically deduce using the Law of Syllogism from the following statements?
If it Spring, then it will rain.
If it will rain, then I will carry an umbrella.
If it is Spring, then I will carry an umbrella.
The sum of 3 angles is 90. What can be said about the anges?
They are complementary.
True or False:
The contrapositive of a conditional is
~q --> ~p
True.