Mathematics Language symbols

___________________ facilitates communication and clarifies meaning. It allows people to express themselves and maintain their identity

Language of Mathematics

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

1. -

2. -

3. -

Precise
Concise
Powerful

In english, ____________ are used to name things we want to talk about; whereas ________________ are used to state complete thoughts

nouns
sentences

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

expression

An _____________ is a name given to a mathematical object of interest. The mathematical analogue of a ‘sentence’ will also be called a _______________

expression
sentence

The _______________ is the object that is being worked on by an operation. Operations can be mathematical ones such as multiplication or addition, or they can be more sophisticated functions

Operand

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

Operands
Operators

__________________ are the objects that are being manipulated

Operands

________________ are the symbols that represent specific actions

Operators

What are the 2 types of operators?

1. -

2. -

Unary
Binary

___________ means operation is performed on one operand

Unary

______________ means operation is performed on two operands

Binary

In mathematics, a __________________ is an operation with only one operand

unary operation

Common notations are __________________, _________________, ________________, and ______________

prefix notation
postfix notation
functional notation
superscripts

What are the 3 Unary operators?

1. -

2. -

3. -

Negation
Reciprocal
Absolute value

_______________ involves reversing the sign of a number

Negation

____________________ involves dividing 1 by the number

Reciprocal

_________________ involves reversing the sign of a number if it is negative and leaving the number unchanged if it is 0 or positive

Absolute value

In mathematics, a ________________ on a set is a calculation that combines two elements of the set (called __________) to produce another element of the set. It is an operation of parity of two whose two domains and one codomain are the same set

Binary operation
Operands

What are the 6 Properties of Binary operations?

1. -

2. -

3. -

4. -

5. -

6. -

Closure of Binary operations
Commutativity of Binary operations
Associativity of Binary operations

Distributive Property of Binary operations
Identity elements of Binary operations
Inverses of Binary Operations

_________________ is a property of binary operation that talks about how the product and sum of any two real numbers is also a real number

Closure of binary operations

________________ is a property of binary operations that talks about how a binary operations is said to be commutative if A CHANGE IN THE ORDER OF ARGUMENTS results in equivalence

Commutativity of binary operations

__________________ is a property of binary operations that talks about how a binary operations is said to be associative if PARENTHESES can be reordered and the result is equivalent

Associativity of Binary operations

_________________ is a property of binary operations that talks about how distributivity applies when multiplication performed on a group of two numbers added or subtracted togeher

Distributive Property of binary operations

_________________ is a property of binary operations that talks about how an element e is said to be an identity element of a binary operations if under the operation any element combined with e results in the same element

Identity elements of Binary operations

The identity element e in addition is ______

0

The identity element e in multiplication is _____

1

_________________ is a property of binary operations that talks about how for an element x, the inverse denoted x^-1 when combined with x under the binary operation results in the identity element for that binary operation

Inverses of binary operations

The inverse element of addition is the _______ of the number and the element of multiplication is the ___________ of the number

negative
reciprocal

____________ is an instrument for appraising the correctness of reasoning

Logic

______________ is a declarative statement that is true or false but NOT BOTH

Proposition

__________________ is a word or symbol that joins two sentences to produce a new one

Logical connectives

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

Truth table

What are the 5 logical connectives in the truth table?

1. -

2. -

3. -

4. -

5. -

Negation
Conjunction
Disjunction
Conditional or Implication
Biconditional or Equivalence

______________

Not P
It is not the case that P
It is false that P
It is not true that P

Negation

We call P and Q a __________ in conjuctions

conjunct

____________

and
moreover

although

still

furthermore

also 

nevertheless

however

yet

but

Conjunction

We call P and Q a _________ in disjuctions

disjunct

___________

or

unless

Disjuction

In conditional or implication, we call P the _________ and Q the __________

hypothesis
conclusion

____________

If P then Q
P implies Q
P only if Q
Q if P
Q follows form P

Conditional or Implication

_____________

P if and only if Q
P is equivalent to Q
P is necessary and sufficient condition for Q

Biconditional or Equivalence