Page 43 - Algebra 1

Determining Closure Over Subtraction
Determine whether each statement is true or false. Give a counterexample for false statements.
a. The set of integers is closed under subtraction.
SOLUTION
The statement is true because the difference of any two integers will be an integer.
b. The set of real numbers is closed under subtraction.
SOLUTION
The statement is true because the difference of any two real numbers will be a real number.
Application: Dive Depth
Nayip collected a water sample at a depth of 23 meters from the surface. He descended another 12 meters to collect a plant sample. Where was Nayip in relation to the surface when he retrieved the plant sample?
SOLUTION
A depth of 23 meters can be written as (-23).
(-23) - 12
= (-23) + (-12) = -35
Nayip was at 35 meters below the surface when he collected the plant sample.
Find each difference.
(Ex 1)
a. 14 - (-22) b. (-7) - 16
c. (-23.4) - 18.72 d. (-_2 )- (-_1 )
Determine whether each statement is true or false. Give a counterexample for false statements.
(Ex 2)
e. f.
g.
(Ex 3)
Example
2
Math Language
A set of numbers is closed under a given operation if the outcome of the operation on any two members of the set is also a member of the set.
Example
3
Lesson Practice
28 Saxon Algebra 1
The set of whole numbers is closed under subtraction. The set of rational numbers is closed under subtraction.
On January 23, 1960, the Trieste dove to a record depth of 37,800 feet below sea level. The record set previously, on January 7th of the same year, was 13,800 feet less than the dive on January 23rd. What was the record set on January 7th in relation to sea level?
36