Conjectures & Counterexamples
make a conjecture about the value of the product of two even numbers
product is an even number
p: Jan. is a fall month. q: Jan has only 30 days
state p v q, and T/F
Inductive or Deductive? Why?
Holly notices that every Sat. her neighbor mows his lawn. Today is Sat. Holly concludes
her neighbor will mow his lawn.
Inductive, pattern
Points that make up a line.
at least 2 - post. 2.1/2.3
the opposite of, a false example
counterexample
Bats are animals that can fly.
Write converse, T/F
If the animal can fly, then it's a bat. F most birds are animals can fly
Inductive or Deductive? Why?
Students at Olivia's HS must have a "B" avg. in order to participate in sports.
Olivia has a "B" avg., so she concludes that she can participate in sports.
Deductive Reasoning, facts, rules
points that make up a plane
at least 3 noncollinear points - post. 2.2/2.4
reasoning that uses a number of specific examples to arrrive at a conclusion
inductive reasoning
Bats are animals that can fly.
Write inverse, T/F counterex.
If the animal is not a bat, then it cannot fly. F birds can fly and and not bats
Given: IF a # is divisible by 4, then the # is divisible by 2. 12 is div. by 2
Con: 12 is divisible by 2
Valid? Law of Detach.? or Syllogism?
valid, Law of Detachment
a midpoint divides a segment into 2 congruent segments
sometimes/always/never?
Always true
determine if T? or F? give counterex.
If <2 and <3 are supplementary <s,
then <2 is 120 and <3 is 60.
False, sample answer <2 = 50 and <3 = 130
Bats are animals that can fly.
Write the contrapositive, T/F counterex.
If the animal can't fly, then it's not a bat.
T
1. If a triangle is a right triangle, then it has an angle measure of 90.
2. If a triangle has an angle measure of 90, then its acute angles are complementary.
Conclude - If a triangle is a right triangle, then its acute angles are complementary,
valid, Law of Syllogism
the intersection of 3 planes is a line
sometimes/always/never?
Sometimes, if 3 planes intersect then their intersection could be a point or line,