Inductive Reasoning
Find the pattern of the following:
4, 12, 36, 108, 324, 972
Pattern: multiply the previous number by 3
Identify p and q:
If an equation is in the form of y=mx+b, then it is written in slope-intercept form.
p: an equation is in the form of y=mx+b
q: it is written in slope-intercept form
what is the meaning of "~"?
~ : not (negation)
ex. ~p --> not p
What should always be in a biconditional statement?
If and only if
What is the pattern of the following sequence:
63, -44.1, 30.87, -21.609
Pattern: multiply by .7
Write the converse of the following conditional:
If you have good grades, then you have a good gpa.
If you have a good gpa, then you have good grades.
Identify p and q from the following inverse:
If you do not go to college, then you will not get a degree.
p: go to college
q: get a degree
If possible, write a true biconditional from the following statement:
If a whole number is a multiple of two, then the whole number is even.
A whole number is a multiple of two if and only if the whole number is even.
Find the pattern and the next two terms:
2, 4, 16, 256
Pattern: square the previous number
Next two terms: 65,536 and 4,294,967,296
Identify p and q from the following converse:
If the shape has four congruent sides, then the shape is a square.
p: the shape is a square
q: the shape has four congruent sides
Write an inverse with the following:
p: the third planet from the sun
q: the planet is Earth
If the planet is not the third from the sun, then the planet is not Earth.
Is the following biconditional true? If not give a counterexample.
An animal is warm-blooded if and only if it is a mammal.
The biconditional is false.
Counterexample: birds are also warm- blooded.
Find the pattern of the following and write the next two terms:
2, 3, 5, 7, 11, 13
Pattern: prime numbers
Next two terms: 17 and 19
Write a conditional and a converse for the following:
p: an angle measures less than 90° but more than 0°
q: the angle is acute
conditional: If an angle measures less than 90° but more than 0°, then the angle is acute.
converse: If an angle is acute, then the angle measures less than 90° but more than 0°.
Find p and q from the following inverse:
If a figure is not three sided, then it is not a triangle.
p: a figure is three sided
q: the figure is a triangle
Write a true biconditional from the following conditional:
If a triangle is isosceles, then it has two congruent sides.
A triangle is isosceles if and only if it has two congruent sides.
Find the pattern and next two terms of the following:
1, 1, 2, 3, 5, 8, 13, 21
Pattern: add the first two numbers to get the third number, then add the second and third to find the fourth number and so on.
Next two numbers: 34 and 55
write a conditional and a converse to the following inverse:
If you do not run for 10 minutes, then you will not raise your heart rate.
conditional: If you run for ten minutes, then you will raise your heart rate.
converse: If you raised your heart rate, you ran for ten minutes.
Write an inverse from the following converse:
If an angle is a right angle, then it measures 90°
If an angle does not measure 90°, then it is not a right angle.
Write two conditionals from the following biconditional:
An animal is a turtle if and only if the animal's scientific name is testudines.
If an animal is a turtle, then its scientific name is testudines.
If an animal's scientific name is testudines, then the animal is a turtle.