12.1-12.3

Question 0

What makes sets equal?

Answer 0

If sets A and B have the same elements, then they are equal

Question 1

What is an empty set?

Answer 1

A set with nothing in it

Symbol: { }

Question 2

What makes sets subsets?

Answer 2

If each element of A is also an element of B, then A is a subset of B

Question 3

What is the symbol to say something is the subset of another.

Answer 3

A c (with a line under it) B

Question 4

What is a proper subset?

Answer 4

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}

Question 5

What is a subset?

Answer 5

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}

Question 6

True or false: an empty set is always a subset of every set

Answer 6

True

Question 7

How do you find out how many subsets you will get?

Answer 7

2^n

N= # of elements

Question 8

What does intersection of A and B look like? And what does it mean?

Answer 8

A (upside down u) B.

Question 9

What does Union of A and B look like? And what does it mean?

Answer 9

A u B

Question 10

What is universal set?

Answer 10

All elements we wish to consider

Symbol: u

Question 11

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)

Answer 11

The compliment of A would be all elements in the universal set but not in set A

Question 12

What is the Counting formula?

Answer 12

If A and B are finite sets then:

n(A u B)= n(A) +n(B) -n(A n B)

Question 13

What is the addition principle of counting?

Answer 13

If sets A and B have no elements in common (disjoint) then:

N(A u B)= n(A) + n(B)

Question 14

What is the equation for an ordered arrangement of r objects chosen from n objects?

Answer 14

N^r = # of arrangements

Question 15

What is the equation for a permutation in which objects are distinct, there is no repetition, and ORDER MATTERS?

Answer 15

P(n,r)

Question 16

What is 0!

Answer 16

1

Question 17

What is the equation for the # of combinations of n distinct objects taken r at a time?

Answer 17

When no repetition and ORDER IS NOT IMPORTANT….

C(n,r)

Question 18

What is the equation for permutations that don’t have distinct objects?

Answer 18

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

Question 19

What would you do for a circular permutation?

Answer 19

(N-1)!

Question 20

What is a sample space?

Answer 20

S (symbol) is the set of all possibilities that can occur

Question 21

What are two truths about probability?

Answer 21

1. Probability is non negative

2. the sum of all probabilities is 1

Question 22

What is the addition rule for probability?

Answer 22

P(E u F)= P(E) + P(F) - P(E n F)

E and F are 2 events

Question 23

What’s the equation if E and F are mutually exclusive (which means they do not occur at the same time)?

Answer 23

P(E u F) = P(E) + P(F)

E and F are two events

Question 24

What is A U A(with a line over it) =?

Answer 24

= universal set

Question 25

A n A(with line over top) =?

Answer 25

No solution