Conjecture
What is the next term in the sequence
1/2, -1/4, 1/8, -1/16.........
1/32
What is the inverse of
If p then q
if not p then not q
Is the bi-conditional true
A polygon is a triangle if and only if the sum of its interior angles is less than 360 degrees
false
If James does work he will pass SS
If James passes summer school then he will raise his GPA
Given: James raised his GPA
conclusion James did his work
Detachment, Syllogism or not valid
not valid
name the property
3(4+5) = 3(4) +3(5)
Distributive property
Is the conjecture T/F if F give counterexample
The sum of two odd numbers is always odd
2, 6, 10 14 ......
What is the converse of
If it is raining then the street is wet
If the street is wet then it is raining
Write the two conditionals as a bi-conditonal
If the sum of two angles is 180 degrees then the angles are supplementary
If two angles are supplementary then the sum of the angles is 180 degrees
Two angles are supplementary if and only if the sum of the angles is 180 degrees.
If it is noon students will go to lunch
If students go to lunch the students will be in the cafeteria
given It is noon
concl: Students are in the cafetria
detachment, Syllogism, not valid
syllogism
Which property justifies the step
1. 4x -7 =19 given
2. 4x = 26 ___________
Addition property
what is the next term, explain your answer
1, 4, 9, 16.........
25 x= n squared
Write the contrapositive of the statement
If an animal is an alligator then it is a reptile
If an animal is not a reptile then it is not an alligator
Two conditionals may be written as a biconditional statement if what two conditions exist
a conditional statement is true
the first statements converse is also true
which property justifies the step
1. x/3 = 2x + 4 given
2. x = 3(2x +4) ______________
multiplication property