Infinite Sets
Sets Q, N, Z are all examples of...
countably infinite sets
When solving GCD problems, we look at the _____ exponent.
smallest
When solving LCM problems, we look at the ______ exponent.
largest
The "code phrase" for set union is...
The "code phrase" for set intersection is...
union = "EITHER/OR"
intersection = "AND"
The definition of a prime number is...
A number that can only be divided by itself and 1.
Explain what it means to say that a set A is "uncountably infinite"
A set A is uncountably infinite if we can not make a complete list of it that makes a 1-1 correspondence with natural numbers N.
To encourage public transportation, Russom wants to give some friends envelopes with bus tickets and subway tickets in them. If he has 18 bus tickets and 12 subway tickets to split equally among the envelopes, and wants no tickets left over, what is the greatest number of envelopes Russom can make?
GCD(18,12) = 6
Miley and Cole ended up making the same number of biscuits for a bake sale at school, even though Miley made them in batches of 24 biscuits and Cole made them in batches of 20 biscuits. What is the smallest number of biscuits each must have baked?
LCM(24, 20) = 120
n(A) refers to the __________ of set A
set size (or cardinality)
True or false?
7 and 9 are relatively prime
Justify your answer.
True. GCD(7,9) = 1
The phrase "infinite decimal expansion" means...
All decimals can be defined to any finite number of decimal places.
The prime decomposition of 72 is...
2^3 × 3^2
The prime decomposition of 75 is...
5^2 x 3^1
Name one of DeMorgan's two laws:
1st law: (A ∪ B)’ = A’ ∩ B’
2nd law: (A ∩ B)’ = A’ ∪ B’
How many divisors does 48 have?
(4+1)(1+1) = 10 divisors
The set of all real numbers R can be described as...
(any of the below answers are suitable)
- decimals
- uncountably infinite
- {non-repeating decimals} U {repeating decimals}
Find GCD(93,27)
GCD(93,27) = 3
Find LCM(36, 50)
LCM(36,50) = 900
A = {65, 33, 175, 29, 12, 122}
B = {44, 82, 13, 122, 67}
C = {20, 125, 155, 33}
Given these sets...
A' n C = ?
A' = {44, 82, 13, 67, 20, 125, 155}
C = {20, 125, 155, 33}
A' n C = {20, 125, 155}
True or false...
We must only test every prime number less than or equal to 13 to figure out if 127 is a prime number
False. We must only test up to prime number 11 to see if 127 is a prime number.
{R \ Q} is...
The set of all irrational numbers
The set of all non-repeating decimals
An uncountably infinite set
GCD(322,147) = 7
Find LCM(63,133)
LCM(63,133) = 1197
Is 329 a prime number? Justify your answer.
No, 329 is not a prime number because it is divisible by 7.