Midterm 1 Flashcards

1
Q

Natural Numbers

A

set of numbers {0,1,2,3…}

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2
Q

Integers

A

{-3,-2,-1,0,1,2,3}

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3
Q

Rational Numbers

A

Denoted by (Q) all numbers which may be written in the form p/q where p and q are integers

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4
Q

Real numbers

A

set of all rational and irrational numbers. and solution to x=sqrt(a) where a is an integer and xi is not rational

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5
Q

b|a

A

a=bx

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6
Q

prime numbers

A

p is prime provided p>1 and the only positive divisors of p are 1 and p

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7
Q

odd numbers

A

an integer a is odd provided there exists an integer x s.t a=2x+1

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8
Q

composite numbers

A

x is a member of the natural numbers >0. x is composite if there exists an integer b st. 1<b><x and b|x</b>

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9
Q

even definition

A

let x be an integer. x is even if 2|x

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10
Q

Conjectures

A

seem to be true but cannot be proven for all

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11
Q

converse of IF A THEN B

A

IF B THEN A

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12
Q

contrapositive of IF A THEN B

A

IF B’ THEN A’

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13
Q

inverse of IF A THEN B

A

IF ‘A THEN ‘B

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14
Q

Simple multiplication principle

A

if we have 2 element lists for which there are n choices for the 1st element and m choices for the 2nd. There are mn possible lists

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15
Q

extended multiplication pinciple

A

supp we have k element list where there are nj choices for the jth elemnt/ then there are n1n2n3..*nk possible lists

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16
Q

cardinality

A

the number of elements in a set

17
Q

B proper subset A

A

there exists an x that is ina but not b

18
Q

the power set

A

denoted 2^A is the set of all subsets of A

19
Q

AuB=BuA AnB=BnA

A

communitive property

20
Q

AuBuC=Au(BuC)

A

assosciative

21
Q

Au(empty set)=

22
Q

An(emptyset)=

23
Q

Au(BnC)=(AuB)n(AuC)

A

distributive

24
Q

inclusion exclusion principle

A

cardinality( AuB)= card(A) + card(B) - card(AnB)

25
set difference B-A
everything in B not in A
26
compliment of A
universe-A
27
Symmetric Difference (A triangle B)
(A-B)u(B-A)
28
Cartesian product AxB
{(a,b): a member of A, b member of B}
29
card(AxB)
card(B) x card(A)
30
Demorgans LAws
A-(BuC)= (A-B) N(A-C) | A-(BnC)=(A-B)u(A-C)
31
relations
a set of ordered pairs
32
x(R)y
means x is related to y
33
inverse relation of R={x,y: (x,y)}
R^(-1)={x,y: (y,x) member of R}
34
reflexive
if for all x in A (x,x) is in R
35
irreflexive
if for all x in A (x,x) is not in R
36
symetric
if (x,y) in R implies (y,x) in R
37
antisymetric
if (x,y) and (y,x) in R then x=y
38
transitive
if (x,y) and (x,z) are in R then (x,z) in R