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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

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2
Q

Components of a Language

A
  • Vocabulary and grammar/rules of symbols or words
  • People who use and understand these symbols/words
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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.)

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4
Q

Math is a ______________________?

A

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

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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
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5
Q

Mathematics uses __________ instead of ______________.

A

symbols, words

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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)

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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

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8
Q

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

A

VERB

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9
Q

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

A

PRONOUNS

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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

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10
Q

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

A

6 + x

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11
Q

Verbal Phrase to Expressions
2. Eight more than a number

A

y + 8

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11
Q

Verbal Phrase to Expressions
3. A number plus five

A

n + 5

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12
Q

Verbal Phrase to Expressions
4. Ten times a number

A

10.n or (10n)

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12
Q

Verbal Phrase to Expressions
5. A number increased by 5

A

x + 7

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13
Q

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

A

6 + x

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14
Q

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

A

6 + x =

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15
Q

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

A

10y

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16
Q

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

A

11m+6

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17
Q

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

A

7k-8

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18
Q

ENGLISH WORDS TO MATHEMATICS
1. Product of two numbers

A

A x B or AB

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19
Q

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

A

2x + 3

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20
Q

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

A

x + y + z >10
_

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21
ENGLISH WORDS TO MATHEMATICS 4. The price of the house increased by 8%
Pnew=Pold + (0.08)(Pold)
22
It is the science of reasoning and help us understand and reason about different mathematical statements.
Logic
23
Every language contains different types of sentences such as statements, questions, and commands.
Logic Statements
24
a statement either true or false but not both
propositions
25
The ____________ of the proposition is the truth and falsify of the statement.
truth value
26
Propositional variables:
p, q, r, s, ...
27
A proposition that is always true
T
28
A proposition that is always false
F
29
If a preposition p is TRUE, its truth value is ________, denoted by __.
True, T
30
If a preposition p is FALSE, its truth value is ________, denoted by __.
FALSE, F
31
Propositions can be divided into?
simple and compound propositions.
32
a proposition that contains no connectives (e.g., not, and, or, if, etc.)
Simple/ Basic proposition
33
composed of simple proposition and logical connectives
Compound Propositions
34
Logical connectives (operators):
Negation, Conjunction, Implication, Disjunction, Biconditional
35
What does this symbol mean? ¬ or ~
Negation
36
What does this symbol mean? ^
Conjunction
37
What does this symbol mean? ↔
Biconditional
37
What does this symbol mean? v
Disjunction
38
What does this symbol mean? →
Implication
39
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
Propositional Connective
40
Propositional Connectives "^" mean?
and (conjunction)
41
Propositional Connectives "v" mean?
or (disjunction)
42
Propositional Connectives "⊕" mean?
or (exclusive or)
43
Propositional Connectives "->" mean?
if then (implication)
44
Propositional Connectives "<->" mean?
if and only if (Biconditional)
45
Propositional Connectives "~/ ¬" mean?
not (negation)
45
Propositions built up by combining propositions using propositional connectives called?
Compound Propositions
46
A collection of objects, which are called elements or members of the set.
SET
47
The truth values of compound propositions can be described by
TRUTH TABLES
48
A table showing what the resulting truth value of a complex statement is for all the possible truth values for the simple statements.
Truth Tables
49
used to determine when a compound statement is true or false
TRUTH TABLES
50
A set which has no question about what elements should be included.
WELL- DEFINED SET
51
What are the steps in writing a set in math?
- 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
SET MEMBERSHIP
-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
Describe the set in words using a verbal statement.
Verbal Description Method
54
This is the form of the set where the elements are all listed, each separated by commas.
Roster Form
55
A formal statement that describes the members of a set is written between the braces.
Set Builder or Set Generator
56
3 Different methods of describing a set
Verbal Description Set builder notation Roster Notation
57
Set name of symbol N
Natural Numbers
58
Set name of symbol W
Whole Numbers
59
Set name of symbol Z
Integers
60
Set name of symbol Q
Rational Number
61
Set name of symbol R
Real Numbers
62
Set name of symbol C
Complex Numbers
63
Finite Set
A set that contains no elements or the number of elements in the set is a natural number
64
A _____ set contains an indefinite (uncountable) number of elements
Infinite
65
____ sets have the exact same elements in them, regardless of their order
Equal
66
" ∅ or { }" is called?
Null set or Empty Set
67
A set that has a symbol n(A)= n (B)
Equivalent Set
68
Universal Set
A set that contains all the elements under consideration
69
The number of elements in set A is its cardinal number
Cardinal Number
70
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 :⊆
SUBSETS
71
It is a technique used for picturing set relationships.
VENN DIAGRAM
72
Two sets which have no elements in common are said to be disjoint.
DISJOINT SETS
73
Type of set that has overlapping area shared by the two circles
OVERLAPPING SETS
74
SYMBOL: ∩
INTERSECTION
75
The ____ of two given sets contains all of the elements for those sets SYMBOL: U
UNION
76
The set known as the complement contains all the elements of the universal set, which are not listed in the given subset.
COMPLEMENT OF A SET
77

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

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