12.1-12.3 Flashcards
What makes sets equal?
If sets A and B have the same elements, then they are equal
What is an empty set?
A set with nothing in it
Symbol: { }
What makes sets subsets?
If each element of A is also an element of B, then A is a subset of B
What is the symbol to say something is the subset of another.
A c (with a line under it) B
What is a proper subset?
This is a set that is not exactly the same as the original. A proper subset is never exactly the same as the original. That would be called just a subset
Ex) A={1,2,3}
(Proper subset) B={1,2}
(Not a proper subset} C={1,2,3}
What is a subset?
This is a set that isn’t exactly the same as the original set or it might be the exact same as the original.
Ex) A={1,2,3}
(Subset) B={1,2}
(Subset) C ={1,2,3}
True or false: an empty set is always a subset of every set
True
How do you find out how many subsets you will get?
2^n
N= # of elements
What does intersection of A and B look like? And what does it mean?
A (upside down u) B.
What does Union of A and B look like? And what does it mean?
A u B
What is universal set?
All elements we wish to consider
Symbol: u
When you have a universal set and set A what would be the compliment of A (with symbol A with a line over the top)
The compliment of A would be all elements in the universal set but not in set A
What is the Counting formula?
If A and B are finite sets then:
n(A u B)= n(A) +n(B) -n(A n B)
What is the addition principle of counting?
If sets A and B have no elements in common (disjoint) then:
N(A u B)= n(A) + n(B)
What is the equation for an ordered arrangement of r objects chosen from n objects?
N^r = # of arrangements
What is the equation for a permutation in which objects are distinct, there is no repetition, and ORDER MATTERS?
P(n,r)
What is 0!
1
What is the equation for the # of combinations of n distinct objects taken r at a time?
When no repetition and ORDER IS NOT IMPORTANT….
C(n,r)
What is the equation for permutations that don’t have distinct objects?
N!/( n1!n2!n3!….)
ex) this would be used when the problem asks how many possible words can be made from the word economics. N in the numerator is 9 and n1 is 2 since c repeats twice and n2 is 2 as well because o repeats
What would you do for a circular permutation?
(N-1)!
What is a sample space?
S (symbol) is the set of all possibilities that can occur
What are two truths about probability?
- Probability is non negative
2. the sum of all probabilities is 1
What is the addition rule for probability?
P(E u F)= P(E) + P(F) - P(E n F)
E and F are 2 events
What’s the equation if E and F are mutually exclusive (which means they do not occur at the same time)?
P(E u F) = P(E) + P(F)
E and F are two events
What is A U A(with a line over it) =?
= universal set
A n A(with line over top) =?
No solution
