Mathematical Languange And Symbols

Question 1

It facilitates communication and clarifies meaning.

Answer 1

Language of Mathematics

Question 2

It allows people to express themselves and maintain their
identity

Answer 2

Language of Mathematics

Question 3

Characteristics of the Language of Mathematics

The language of mathematics makes it easy to express the
kinds of thoughts that mathematicians like to express. It is:

Answer 3

• Precise
• Concise
• Powerful

Question 4

Mathematical Symbols

Σ

Answer 4

the sum of

Question 5

Mathematical Symbols

Ǝ

Answer 5

there exists

Question 6

Mathematical Symbols

ꓯ

Answer 6

for every (for any)

Question 7

Mathematical Symbols

Є

Answer 7

element of

Question 8

Mathematical Symbols

⊆

Answer 8

subset of

Question 9

Mathematical Symbols

⇒

Answer 9

if …., then

Question 10

Mathematical Symbols

⇔

Answer 10

if and only if

Question 11

Mathematical Symbols

ℛ or ℜ or ℝ

Answer 11

set of real numbers

Question 12

Mathematical Symbols

ℕ

Answer 12

set of natural numbers

Question 13

Mathematical Symbols

ℤ

Answer 13

set of integers

Question 14

Mathematical Symbols

ℚ

Answer 14

set of rational numbers

Question 15

In English, ________ are used to name things we want to talk about (like people, places, and things); whereas sentences are used to state complete thoughts.

Answer 15

Nouns

Question 16

• A typical English sentence has at least _______ , and at least _____.

Answer 16

One noun
One Verb

Question 17

MATHEMATICS: expressions versus sentences

The mathematical analogue of a ‘noun’ will be called an __________

Answer 17

Expression

Question 18

it is a name given to a mathematical object of interest.

Answer 18

Expression

Question 19

• The mathematical analogue of a ‘sentence’ will also be called a _________.

Answer 19

Sentence

Question 20

‘=‘ is

Answer 20

Verb

Question 21

The ________ is the object that is being worked on by an operation.

Answer 21

Operand

Question 22

___________ can be mathematical ones such as multiplication or
addition, or they can be more sophisticated functions.

Answer 22

Operations

Question 23

Operations can be mathematical ones such as ______________ or _____________, or they can be more ____________ functions.

Answer 23

Multiplication
Addition
Sophisticated

Question 24

In all computer languages, expressions consist of two types of components:

Answer 24

Operators
Operands

Question 25

________ are the objects that are manipulated

Answer 25

Operands

Question 26

__________ are the symbols that represent specific actions.

Answer 26

Operators

Question 27

5 + x x and 5 are __________ + is an ________

Answer 27

Operands Operators

Question 28

Types of Operators

Answer 28

Unary Binary

Question 29

It means operation performed on one operand

Answer 29

Unary

Question 30

It means operation is performed on two operands

Answer 30

Binary

Question 31

is an operation with only one operand, i.e. a single input.

Answer 31

Unary operation

Question 32

are prefix notation (e.g. +, −, ¬), postfix notation (e.g. factorial n!), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well.

Answer 32

Common notations

Question 33

In common arithmetic, the unary operators are:

Answer 33

negation reciprocal absolute value

Question 34

____________ involves reversing the sign of a number.

Answer 34

Negation

Question 35

it involves dividing 1 by the number.

Answer 35

Reciprocal

Question 36

The _____________ involves reversing the sign of a number if it is negative, and leaving the number unchanged if it is 0 or positive.

Answer 36

Absolute value

Question 37

a set is a calculation that combines two elements of the set (called________) to produce another element of the set.

Answer 37

Binary operation Operands

Question 38

a______________ is an operation of parity (the number of arguments or operands that the function takes) of two whose two _____ and one _________ are the same set.

Answer 38

binary operation domains codomain

Question 39

PROPERTIES OF BINARY OPERATIONS

Answer 39

1. **Closure** of Binary Operations 2. **Commutativity** of Binary Operations 3. **Associativity** of Binary Operations 4. **Distributivity** of Binary Operations 5. **Identity** **Elements** of Binary Operations 6. **Inverses** of Binary Operations

Question 40

A Binary Operations that product and the sum of any two real numbers is also a real number. In symbols, we write

Answer 40

Closure of Binary Operations

Question 41

What binary operation is said to be ________ if a change in the order of the arguments results in equivalence?

Answer 41

Commutativity of Binary Operations Commutative

Question 42

What binary operation is said to be ________ if parentheses can be reordered and the result is equivalent?

Answer 42

Associative Associativity of Binary Operations

Question 43

________________applies when multiplication is performed on a group of two numbers added or subtracted together

Answer 43

Distributivity of Binary Operations

Question 44

An element "e" is said to be an ____________ (or neutral element) of a binary operation if under the operation any element combined with "e" results in the same element.

Answer 44

Identity Elements of Binary Operations

Question 45

For an element x, the ____ denoted x1 when combined with x under the binary operation results in the identity element for that binary operation.

Answer 45

Inverses of Binary Operations

Question 46

is an instrument for appraising the correctness of reasoning.

Answer 46

Logic

Question 47

is a declarative statement that is true or false but not both.

Answer 47

proposition P

Question 48

is a table that shows the truth value of a compound statement for all possible truth values of its simple statements.

Answer 48

Truth Table

Question 49

it is if the word is not introduced in the negative statement.

Answer 49

NEGATION

Question 50

A word or symbol that joins two sentences to produce a new one.

Answer 50

LOGICAL CONNECTIVES