Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

GEED 004- Mathematics in the Modern World > Module 2 > Flashcards

Module 2 Flashcards

1
Q

What is “Language”?

A

A systematic means of communicating ideas or feelings by the use of conventional symbols, sounds, or marks

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Components of a Language

A
  • Vocabulary and grammar/rules of symbols or words
  • People who use and understand these symbols/words
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Why Math is a Language?

A

Mathematics meets this definition of a language.
(Linguists who don’t consider math a language cite its use as a written rather than spoken form of communication.)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Math is a ______________________?

A

Universal Language (The symbols and organization to form
equations are the same in every country of the world.)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

3 Characteristics of the Language of Math

A
  1. PRECISE - able to make very fine distinctions
  2. CONCISE - able to say things briefly
  3. POWERFUL - able to express complex thoughts with relative ease
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Mathematics uses __________ instead of ______________.

A

symbols, words

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Often (but not always) letters have special uses:
Those are not rules, but they are often used that way.

A

Start of the alphabet: a, b, c, … means constants (fixed values)

From i to n: i, j, k, l, m, n means Positive integers (for counting)

End of the alphabet: … x, y, z means variables (unknowns)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

________ in math language could be fixed things, such as numbers, or expressions with numbers:
Ex: 15, 2(3-1/2), 4^2

A

NOUNS

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

_______ in math language could be the equals sign “=”, or
an inequality like < or >

A

VERB

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

_______ in math could be variables like x or y:
Ex: 5x-7, xy2, -3/x

A

PRONOUNS

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

EXPRESSION VS. EQUATION

A

Expression - group or number/variable with or without mathematical operation
Equation - group or number/variable with or without mathematical operation SEPARATED by an EQUAL SIGN

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Verbal Phrase to Expressions
1. The sum of six and a number

A

6 + x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Verbal Phrase to Expressions
2. Eight more than a number

A

y + 8

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Verbal Phrase to Expressions
3. A number plus five

A

n + 5

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Verbal Phrase to Expressions
4. Ten times a number

A

10.n or (10n)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Verbal Phrase to Expressions
5. A number increased by 5

A

x + 7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

VERBAL MODEL
Phrase to Expression
The sum of six and a number

A

6 + x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

VERBAL MODEL
Phrase to Expression
The sum of six and a number “is”

A

6 + x =

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

PHRASE TO MATHEMATICAL EXPRESSION
1. The product of 10 and y

A

10y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

PHRASE TO MATHEMATICAL EXPRESSION
2. 6 added to the product of 11 and m

A

11m+6

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

PHRASE TO MATHEMATICAL EXPRESSION
3. 8 less than 7 times k

A

7k-8

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

ENGLISH WORDS TO MATHEMATICS
1. Product of two numbers

A

A x B or AB

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

ENGLISH WORDS TO MATHEMATICS
2. Three more than twice a number

A

2x + 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

ENGLISH WORDS TO MATHEMATICS
3. The sum of three distinct number is at least 10

A

x + y + z >10
_

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

ENGLISH WORDS TO MATHEMATICS
4. The price of the house increased by 8%

A

Pnew=Pold + (0.08)(Pold)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

It is the science of reasoning and help us understand and reason about different mathematical statements.

A

Logic

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Every language contains different types of sentences
such as statements, questions, and commands.

A

Logic Statements

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

a statement either true or false but not both

A

propositions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

The ____________ of the proposition is the truth and falsify of the statement.

A

truth value

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Propositional variables:

A

p, q, r, s, …

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

A proposition that is always true

A

T

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

A proposition that is always false

A

F

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

If a preposition p is TRUE, its truth value is ________, denoted by __.

A

True, T

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

If a preposition p is FALSE, its truth value is ________, denoted by __.

A

FALSE, F

31
Q

Propositions can be divided into?

A

simple and compound propositions.

32
Q

a proposition that contains no connectives (e.g., not, and, or, if, etc.)

A

Simple/ Basic proposition

33
Q

composed of simple proposition and logical connectives

A

Compound Propositions

34
Q

Logical connectives (operators):

A

Negation, Conjunction, Implication, Disjunction, Biconditional

35
Q

What does this symbol mean? ¬ or ~

A

Negation

36
Q

What does this symbol mean? ^

A

Conjunction

37
Q

What does this symbol mean? ↔

A

Biconditional

37
Q

What does this symbol mean? v

A

Disjunction

38
Q

What does this symbol mean? →

A

Implication

39
Q

an operation that combines two propositions to yield a new one whose truth value depends only on the truth values of the two original propositions

A

Propositional Connective

40
Q

Propositional Connectives “^” mean?

A

and (conjunction)

41
Q

Propositional Connectives “v” mean?

A

or (disjunction)

42
Q

Propositional Connectives “⊕” mean?

A

or (exclusive or)

43
Q

Propositional Connectives “->” mean?

A

if then (implication)

44
Q

Propositional Connectives “<->” mean?

A

if and only if (Biconditional)

45
Q

Propositional Connectives “~/ ¬” mean?

A

not (negation)

45
Q

Propositions built up by combining propositions using propositional connectives called?

A

Compound Propositions

46
Q

A collection of objects, which are called elements or members of the set.

A

SET

47
Q

The truth values of compound propositions can be
described by

A

TRUTH TABLES

48
Q

A table showing what the resulting
truth value of a complex statement is
for all the possible truth values for the simple statements.

A

Truth Tables

49
Q

used to determine when a compound statement is true or false

A

TRUTH TABLES

50
Q

A set which has no question about what elements should be included.

A

WELL- DEFINED SET

51
Q

What are the steps in writing a set in math?

A
  • List the elements in the set,
  • Separate each element in the set using a comma,
    -Enclose the elements in the set using curly braces, {}.
52
Q

SET MEMBERSHIP

A

-We use the symbol ∈ to show that an object is a
member of a set.
We use the symbol ∉ to show that an object is not a member of a set.

53
Q

Describe the set in words using a verbal statement.

A

Verbal Description Method

54
Q

This is the form of the set where the elements are all
listed, each separated by commas.

A

Roster Form

55
Q

A formal statement that describes the members of a set
is written between the braces.

A

Set Builder or Set Generator

56
Q

3 Different methods of describing a set

A

Verbal Description
Set builder notation
Roster Notation

57
Q

Set name of symbol N

A

Natural Numbers

58
Q

Set name of symbol W

A

Whole Numbers

59
Q

Set name of symbol Z

A

Integers

60
Q

Set name of symbol Q

A

Rational Number

61
Q

Set name of symbol R

A

Real Numbers

62
Q

Set name of symbol C

A

Complex Numbers

63
Q

Finite Set

A

A set that contains no elements or the number of elements in the set is a natural number

64
Q

A _____ set contains an indefinite (uncountable) number of elements

A

Infinite

65
Q

____ sets have the exact same elements in them, regardless of their order

A

Equal

66
Q

” ∅ or { }” is called?

A

Null set or Empty Set

67
Q

A set that has a symbol n(A)= n (B)

A

Equivalent Set

68
Q

Universal Set

A

A set that contains all the elements under consideration

69
Q

The number of elements in set A is its cardinal number

A

Cardinal Number

70
Q

A set is a subset of a given set if and only if all elements of the subset are also elements of the given set.

SYMBOL :⊆

A

SUBSETS

71
Q

It is a technique used for
picturing set relationships.

A

VENN DIAGRAM

72
Q

Two sets which have no elements in common are said
to be disjoint.

A

DISJOINT SETS

73
Q

Type of set that has overlapping area shared
by the two circles

A

OVERLAPPING SETS

74
Q

SYMBOL: ∩

A

INTERSECTION

75
Q

The ____ of two given sets contains all of the elements for those sets
SYMBOL: U

A

UNION

76
Q

The set known as the complement contains all
the elements of the universal set, which are not listed in the given subset.

A

COMPLEMENT OF A SET

77
Q
A

GEED 004- Mathematics in the Modern World (2 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions