MMW Prelims

Language

is a complex system of words and symbols, either spoken or written, used by a particular community as a means of communication

Precise; Concise; Powerful

Characteristics of the language of mathematics

Precise

able to make very fine distinctions

Concise

able to say things briefly

Powerful

able to express complex thoughts with relative ease

Expression

is the mathematical analog for noun. it is a name given to mathematical object of interest

Sentence

is the mathematical analog for sentence that must state a complete thought

Set

is a collection of objects

Elements

it is the members of a set

Functions

is a mathematical transform of such a kind

equals; is an element of

two other examples of relations

Logical Connective (Logical Operator)

is a symbol or a word which is used to connect two or more sentences. it can be expresses as a truth function

Negation

is the opposite of a statement, usually employing the word not

~

symbol of negation

Negation of statement

Today is Monday = Today is not Monday

Conjunction

is a compound sentence formed by using the word and to join two simple sentences

⋀

symbol of conjunction

Compound sentence: Conjunction

𝑝: Mariella eats fries. 𝑞: Mae drinks soda. = 𝑝 ∧ 𝑞: Mariella eats fries and Mae drinks soda.

Disjunction

is a compound sentence formed by using the word or to join two simple sentences

Compound Sentence: Disjunction

𝑝: The clock is slow. 𝑞: The time is correct. =𝑝 ∨ 𝑞: The clock is slow or the time is correct

V

symbol of disjunction

Implication

is a type of relationship between two statements or sentences.

⇒

symbol of implication

statement of implication

𝑝: Helen finishes her homework. 𝑞: Helen cleans her room.

=

𝑝 ⇒ 𝑞: If Helen finishes her homework, then she will clean her room.

𝑝 ⇒ 𝑞: Helen will clean her room, if she finish her homework.