Definitions of Logic
What do we call an if-then statement?
Conditional Statement
Write the number that comes next:
1, 3, 6, 10, 15, ____
21
Write the converse of the following:
"If a number is even, then it is divisible by 2."
If a number is divisible by 2, then it is even."
Give the conclusion using law of detachment.
1. If today is Friday, then we don't have school tomorrow.
2. Today is Friday.
We don't have school tomorrow.
What property is being demonstrated by:
AB = AB
Reflexive
What is the first part of a conditional statement called (Hint: like in science class before you do an experiment)?
The hypothesis
Write down the number that comes next:
5, 20, 80, ___
320
Write the biconditional of the following statement:
"If a number is even, then it is divisible by 2."
A number is even if and only if it is divisible by 2.
Give the conclusion using the law of syllogism.
1.If 4x = 12, then x = 3
2. If x = 3, then 2x = 6
If 4x = 12, then 2x = 6
What property is being demonstrated?
If XY +PQ = 20 and XY = 5, then 5 + PQ = 20?
Substitution
What are the two types of reasoning we learned?
Deductive and Inductive
Write down the number that comes next:
7, 7/2, 7/4, ____
7/8
Write a counterexample for the following statement:
If a number is positive, then it is greater than or equal to 1.
Any fraction, or decimal, less than 1 but greater than 0.
Write a conjecture about the product of an odd and even number with two examples.
The product of an odd and even number is always even.
If <ABC is being bisected by ray BD, then write a relationship between m<ABD and m<CBD.
m<ABD = m<CBD
What is Inductive reasoning based upon?
Patterns and observations
Write down the number that comes next:
4,8,16,32, ___
64
Write the converse, inverse, and contrapositive of the following statement. Determine the truth value for each.
"If an angle's measure is 34, then it is an acute angle.
Converse: If an angle is acute, then its measure is 34 degrees. - False
Inverse: If angle's measure is not 34 degrees, then it is not acute. - False
Contra: If an angle is not acute, then its measure is not 34 degrees. - True
<1 and <2 are supplementary angles and <1 and <4 are also supplementary angles. What must be true about <2 and <4?
They have the same measure (they are congruent)
What property is being demonstrated?
If AB = MN and MN =ST, then AB = ST ?
The Transitive
Explain the difference between inductive and deductive reasoning.
Inductive is based on patterns and observations
Deductive is based on facts, rules, definitions, laws of logic.
Write an if-then statement whose converse is always true.
Example: If a polygon is regular, then it is equilateral and equiangular.
Rewrite the definition "Supplementary angles are two angles that add up to 180 degrees" as a biconditional.
Two angles are supplementary if and only if, they add up to 180 degrees.
True or False
If line m bisects straight <ABC then two complementary angles are created.
False - they are supplementary
<A and <B are a linear pair. The m<A = 2x - 8 and the m<B = 4x +2. What are the two angle measures?
m<A = 54 degrees
m<B = 126 degrees
x=31 because 2x-8 + 4x+2 = 180 so 6x-6=180 and then 6x=186.