discrete test 2

Question 1

set

Answer 1

unordered collection of elements shown as xEs

Question 2

sets are equal

Answer 2

if and only if they have the same elements number and order do not matter

Question 3

cardinality |s|

Answer 3

the number of elements of the set (repetitions dont add anything

Question 4

a is a subset of b iff (sideways u greater than thing

Answer 4

every element of a is in b

Question 5

P(a)

Answer 5

the power set is the set of all subsets.

Question 6

Cartesian products

Answer 6

A x B (write it you bastard)

Question 7

union aUb

Answer 7

set of all elements in a or b and both aUb

Question 8

intersection anb

Answer 8

just things that are in both a and b

Question 9

symmetric difference(+)

Answer 9

denoted a (+) b

Question 10

a - b

Answer 10

everything in a that isnt in b

Question 11

a-

Answer 11

everything not in a

Question 12

domain of a function

Answer 12

input set

Question 13

range of a funciton

Answer 13

output set

Question 14

one to one

Answer 14

if no output values get mapped to any input values

Question 15

onto

Answer 15

if every element of the output is mapped to some input

Question 16

bijection

Answer 16

both one to one and onto

Question 17

prove that it is a bijection

Answer 17

1. prove one to one by setting equation equal to itself and canceling until x = x.
2. prove that it is onto by solving for x separately in terms of y and plugging that in for x to get y = y

Question 18

floor

Answer 18

round down

Question 19

cieling

Answer 19

round up

Question 20

geometric sequence

Answer 20

terms in a sequence can be found by multiplying by common number r
an = a0(r^n)

Question 21

arithmetic sequences

Answer 21

terms in a sequence can be found by adding a common number d

an = a0 + (dn)

Question 22

does it satisfy the recurrence relation

Answer 22

plug it in

Question 23

find the sum of k as we go to n

Answer 23

n(n+1)/2

Question 24

modular arithematic

Answer 24

a|b iff ak = b for some k

Question 25

prime factorizations

Answer 25

make a tree of multiples down to primes

Question 26

find the gcd

Answer 26

1. get the prime factorization

2. get the smallest powers of the ones that they both share

Question 27

find the lcm of each

Answer 27

take the larger power of each item. dont bother with repititons