RAH

Question 1

An example that proves a statement false is often called a

Answer 1

counterexample

Question 2

direct approach to proving a conditional of the form “if A then B” starts with the assumption that the antecedent ______________

Answer 2

A is true.

Question 3

is a false statement

Answer 3

contradiction

Question 4

starts out by assuming that the statement to be proved is
false

Answer 4

proof by contradiction

Question 5

another name for proof by contradiction

Answer 5

indirect proof

Question 6

a smallest number for which a case is false

Answer 6

minimal counterexample

Question 7

construct an instance of
the object

Answer 7

Constructive approach

Question 8

where we check that each thing has the stated property.

Answer 8

Exhaustive checking

Question 9

That if the premise is true, then the conclusion must also be true.

Answer 9

conditional proof

Question 10

We’ll simply say that a set is a collection of things called its

Answer 10

elements,
members, or objects.

Question 11

A set with one element is called a

Answer 11

singleton

Question 12

Sets can have other sets as elements
T or F

Answer 12

T

Question 13

The set with no elements is called the

Answer 13

empty set or null set

Question 14

The empty set is denoted by

Answer 14

∅ or {}

Question 15

is a set or not?

x = {1,2,3,4,5,…}

Answer 15

yes

Question 16

is a set or not?

x = {1,2,3,…, 35, 37}

Answer 16

yes

Question 17

equal or not

{u,g,h} = {h,u,g}

Answer 17

equal

Question 18

equal or not
{h,g, u,h} = {h, g, u}

Answer 18

not

Question 19

are repeated occurences allowed in sets

Answer 19

no

Question 20

What are natural numbers?

Answer 20

N={0,1,2,3,4,5,…}

Question 21

What are integers?

Answer 21

Z = {…,-2,-1,0,1,2,…}

Question 22

What are rational numbers?

Answer 22

Q={…, -1/2, 0, .08,…}

Question 23

What are real numbers?

Answer 23

R={…,-2, -1/2, 0, .08, 3, √3, π(22/7),…}

Question 24

If A ⊆ B and there is some element in B that does not occur in A,

Answer 24

proper subset

A ⊂ B

Question 25

The collection of all subsets of a set is called the

Answer 25

power set

Question 26

what is the powerset of S = {a, b, c}

Answer 26

S = {∅, {a}, {b}, {c}, {a,b}, {a,c},..., {a,b,c}}

Question 27

consists of one or more closed curves in which the interior of each curve represents a set.

Answer 27

Venn Diagram

Question 28

who created the Venn Diagram

Answer 28

John Venn

Question 29

___________ of two sets A and B is the set of all elements that are either in A or in B or in both A and B

Answer 29

union A U B

Question 30

The _________ of two sets A and B is the set of all elements that are in both A and B

Answer 30

intersection A ∩ B

Question 31

If A ∩ B = ∅, then A and B are said to be

Answer 31

disjoint

Question 32

is the set of elements in A that are not in B

Answer 32

Difference (relative complement) A-B

Question 33

is the set of elements in A that are not in B, and in B but not in A

Answer 33

symmetric difference

Question 34

the difference U − A is called the

Answer 34

complement A'

Question 35

The size of a set S is called its

Answer 35

cardinality

Question 36

) is a collection of objects that may contain repeated occurrences of elements

Answer 36

bag (or multiset

Question 37

T or F there is order and arrangement in bags or multisets

Answer 37

F

Question 38

equal or not? Bag ed. [h,u,g,h] = [h,u,g]

Answer 38

NOT

Question 39

is the first one a subbag of the second? [a, b,a] ⊆ [a, b]

Answer 39

NOPE

Question 40

T OR F | There is no order in sets

Answer 40

T

Question 41

What is the Inclusion-Exclusion principle

Answer 41

|A ∪ B| = |A| + |B| − |A ∩ B|

Question 42

is a collection of things, called its elements, where there is a first element, a second element, and so on.

Answer 42

Tuple

Question 43

What are the things inside tuples called?

Answer 43

members

Question 44

The 0-tuple is denoted by ___________

Answer 44

( ), and we call it the empty tuple

Question 45

2-tuple is often called an

Answer 45

ordered pair

Question 46

equal or not. (3,7) = (7,3)

Answer 46

NOT IT IS TUPLE STUPIT

Question 47

Characteristic of tuple?

Answer 47

Yes repeat is good YES ARRANGEMENT MATTERS

Question 48

is denoted by A × B, is the set of all ordered pairs (a, b)

Answer 48

Cartesian product

Question 49

can be thought of as a table of objects that are indexed by rows and columns

Answer 49

Matrix

Question 50

finite ordered sequence of zero or more elements that can be repeated.

Answer 50

List

Question 51

what’s the difference between tuples and lists?

Answer 51

tuples, we can randomly access any component in a constant amount of time. lists, we can randomly access only two things in a constant amount of time. (Heads and tails)

Question 52

number of elements in a list is called its

Answer 52

length

Question 53

Whyat is the heads and tails of

Answer 53

heads = tails =

Question 54

will be used to denote this construction operation

Answer 54

cons

Question 55

A = B = What is cons(head(A), head(B)) ?

Question 56

A = B = What is cons(A, B) ?

Answer 56

< ,N, r,t,y,j>

Question 57

he block of memory contains the element together with an address

Answer 57

(called a pointer or link

Question 58

is a finite ordered sequence of zero or more elements that are placed next to each other in juxtaposition

Answer 58

string

Question 59

make up a string are taken from a finite set called

Answer 59

Alphabet

Question 60

string over of {a,b,c}

Answer 60

a, bc, abba, bbcba

Question 61

string with no element is called the

Answer 61

empty string

Question 62

is a set of strings

Answer 62

language

Question 63

is a written number.

Answer 63

numeral

Question 64

represent the set of positive integers by using the alphabe

Answer 64

Roman numerals

Question 65

set of natural numbers using the alphabet

Answer 65

decimal numerals

Question 66

represent the natural numbers using the alphabet

Answer 66

Binary numbers

Question 67

We can combine two languages L and M to obtain the set of all concatenations of strings in L with strings in M

Answer 67

Product of languages

Question 68

L = {ab, ac} M = {a, bc, abc} LM = ?

Answer 68

{aba, abbc, ababc, aca, acbc, acabc}

Question 69

is a set of n-tuples, where the elements in each tuple are related in some way.

Answer 69

Relation

Question 70

Another term for 1-ary, 2-ary, and 3-ary,

Answer 70

unary, binary, and ternary

Question 71

is a collection of facts that are represented by tuples such that the tuples can be accessed in various ways to answer queries about the facts.

Answer 71

relational database

Question 72

What is product rle?

Answer 72

|A × B| = |A||B|

Question 73

informal proof is a demonstration that some statement is true

Answer 73

informal proof