Midterm 1

Question 1

Natural Numbers

Answer 1

set of numbers {0,1,2,3…}

Question 2

Integers

Answer 2

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

Question 3

Rational Numbers

Answer 3

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

Question 4

Real numbers

Answer 4

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

Question 5

b|a

Answer 5

a=bx

Question 6

prime numbers

Answer 6

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

Question 7

odd numbers

Answer 7

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

Question 8

composite numbers

Answer 8

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>

Question 9

even definition

Answer 9

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

Question 10

Conjectures

Answer 10

seem to be true but cannot be proven for all

Question 11

converse of IF A THEN B

Answer 11

IF B THEN A

Question 12

contrapositive of IF A THEN B

Answer 12

IF B’ THEN A’

Question 13

inverse of IF A THEN B

Answer 13

IF ‘A THEN ‘B

Question 14

Simple multiplication principle

Answer 14

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

Question 15

extended multiplication pinciple

Answer 15

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

Question 16

cardinality

Answer 16

the number of elements in a set

Question 17

B proper subset A

Answer 17

there exists an x that is ina but not b

Question 18

the power set

Answer 18

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

Question 19

AuB=BuA AnB=BnA

Answer 19

communitive property

Question 20

AuBuC=Au(BuC)

Answer 20

assosciative

Question 21

Au(empty set)=

Answer 21

A

Question 22

An(emptyset)=

Answer 22

empty set

Question 23

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

Answer 23

distributive

Question 24

inclusion exclusion principle

Answer 24

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

Question 25

set difference B-A

Answer 25

everything in B not in A

Question 26

compliment of A

Answer 26

universe-A

Question 27

Symmetric Difference (A triangle B)

Answer 27

(A-B)u(B-A)

Question 28

Cartesian product AxB

Answer 28

{(a,b): a member of A, b member of B}

Question 29

card(AxB)

Answer 29

card(B) x card(A)

Question 30

Demorgans LAws

Answer 30

A-(BuC)= (A-B) N(A-C)

A-(BnC)=(A-B)u(A-C)

Question 31

relations

Answer 31

a set of ordered pairs

Question 32

x(R)y

Answer 32

means x is related to y

Question 33

inverse relation of R={x,y: (x,y)}

Answer 33

R^(-1)={x,y: (y,x) member of R}

Question 34

reflexive

Answer 34

if for all x in A (x,x) is in R

Question 35

irreflexive

Answer 35

if for all x in A (x,x) is not in R

Question 36

symetric

Answer 36

if (x,y) in R implies (y,x) in R

Question 37

antisymetric

Answer 37

if (x,y) and (y,x) in R then x=y

Question 38

transitive

Answer 38

if (x,y) and (x,z) are in R then (x,z) in R