Inductive Reasoning
Find the next item in the pattern
March, May, July,____
September
What is a biconditional statement?
A statement that can be written in the form "p if and only if q"
Solve the equation -5=3n+1; Use each property for proof.
Show proof.
What is a conditional statement in the simplest terms?
If P, then Q
Complete the conjecture:
The product of two even terms is_____
even
Write the definition as a biconditional.
A triangle is a three-sided polygon.
A figure is a triangle if and only if it a three sided polygon
Reflexive Property, Symmetric, Transitive
Identify the hypothesis and conclusion of the given statement:
If a person is at least 16 years old, then the person can drive a car.
Hypothesis: If a person is at least 16 years old
Conclusions: Then the person can drive a car
Show that the conjecture is false by showing a counterexample:
1-y>0 then 0<y<1
y=-1
Write the conditional statement and converse within each biconditional.
Perry can paint the entire living room if and only if he has enough paint
A triangle has 3 sides and 3 vertices. A quad has 4 sides and 4 vertices.
Identify the property that justifies each statement:
1.) x=y so y=x
2.)m<1=m<2, and m<2=m<4, so m<1=m<4
Symmetric,Transitive
Write a conditional statement from the sentence given:
Eighteen year-olds are eligible to vote.
If a person is eighteen then they are eligible to vote
Make a conjecture about each pattern and write the next two items:
-3,6,-9,12,____,____
Multiples of three with alternative signs: -15,18
Determine if the biconditional is true, if false give a counterexample.
The number 2n is even if and only if n is an integer.
True
Use the indicated property to justify each statement. Reflexive Property of Equality:3x-1=___?
Transitive Property of Equality: If m<A=m<X and m<X=m<T then_____?
3x-1, <A=<T
Determine if the conditional statement is true, if false give a counterexample:
If two planes intersect, then they intersect at exactly one point.
False, they intersect at a line
Determine if the conjecture is true, if not prove with a counterexample:
In a triangle with a right angle, the other two sides are congruent
F, with example
Determine if the biconditional is true, if false give a counterexample.
If a=b, then |a|=|b|
False. a=3,b=-3
Solve the equation and write each justification out:
1/2*(p-16)=13
Write the converse, inverse and contrapositive of the following conditional statement. Find whether it is true or false for each statement.
If Brielle drives exactly at 30mi/h, then she travels 10 mi in 20min
Converse: If Brielle travels 10mi in 20min, then she drives exactly at 30mi/h False
Inverse: If Brielle does not drive exactly at 30 mi/h, then she does not travel 10mi in 20min F
Contrapositive: If Brielle does not travel 10mi in 20 min. then she does not drive exactly at 30mi/h True