Converse, Inverse, Contrapositive
Write the given statement in If-Then form.
Today is Thursday, so I have a test.
If today is Thursday, then I have a test.
True or false (if false say why):
An even times an even is always even!
True
1, 2, 4, 8, 16,...
Double the previous term
Prove: x = 6
2x+1 = 13 (Given)
2x = 12 (Subtraction)
x = 6 (division)
Name the reason:
6y = 6y
Reflexive Property
Find the converse of the given statement.
If I put my shoes on wrong, then my feet will hurt.
If my feet hurt, then I put my shoes on wrong.
True or false (give a counterexample if false)
The product of two even numbers is always divisible by 4.
True
100, 10, 1
Divide by 10 each time
Given: 3x + 3 = 4x - 9
Prove: x = 12
3x + 3 = 4x - 9 (Given)
3x + 12 = 4x (Addition)
12 = x (subtraction)
x = 12 (symmetric)
12x + 14 = 8x -16
12x + 30 = 8x
Addition
If today is Monday, then I don't have to worry about my ALEK.
If today is NOT Monday, then I do need to worry about my ALEK.
True or false (give a counterexample if false)
The product of two numbers is always larger than either number.
False; 0* 5 = 0 or 2 * (1/2) = 1
a, c, f, j, ...
Alphabet, skipping one letter more each time.
Given: (2+5x)/3 = 9
Prove: x = 5
(2+5x)/3 = 9 (Given)
2+5x = 27 (Multiplication)
5x = 25 (Subtraction)
x = 5 (Division)
8(x + y) = 8x + 8y
Distribution
Find the contrapositive of the given statement.
If I study, then I will do well on my math test.
If I don't do well on my math test, then I didn't study.
True or False (give a counterexample if false)
All states have more than 2 syllables.
False; Maine
January, March, May, July, August, October, December
Listing months with 31 days
Given: x/3 + 10 = 5
Prove: x = -15
x/3 + 10 = 5 (Given)
x/3 = -5 (subtraction)
x = -15 (multiplication)
3x = 15
x = 5
Division
Is the converse of this statement true?
If I have a good grade in this class, then I did all my homework.
If I did all my homework, then I will have a good grade in this class. (YES!)
True or False (provide an example if false)
Squaring a number and adding one will always provide you with an even number.
False; 42+1 = 17, or 102+1 = 101
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...
Perfect squares
6x/7 - 10 = -4
Prove x = 7
6x/7 - 10 = -4 Given
6x/7 = 6 (Addition)
6x = 42 (Multiplication)
x = 7 (Division)
a = 8 and a = b
b = ?
Transitive