Conjunctions
T+T=
T+F=
F+T=
F+F=
T
F
F
F
Disjunctions
T+T=
T+F=
F+T=
F+F=
T
T
T
F
Conditional Statements
T+T=
T+F=
F+T=
F+F=
T
F
T
T
Biconditional Statements
T+T=
T+F=
F+T=
F+F=
T
F
F
T
facilitates communication and
clarifies meaning
Language of
Mathematics
The language of
mathematics is
- Precise
*Concise - Powerful
The object that is being worked on by
an operation.
OPERAND
EX:
5 + x (x and 5 are operands and + is an operator)
The product and the sum of any two real numbers is
also a real number
EX: 1+1=2
Closure of Binary Operations
A binary operation is said to be commutative if a
change in the order of the arguments results in
equivalence.
Example:
1 + 2 = 2 + 1
2 ∙ 3 = 3 ∙ 2
Commutativity of Binary Operations
A binary operation is said to be associative if parentheses
can be reordered and the result is equivalent.
Example:
𝟏 + 𝟐 + 𝟑 = 𝟏 + 𝟐 + 𝟑
𝟐 ∙ 𝟑 ∙ 𝟒 = 𝟐 ∙ (𝟑 ∙ 𝟒)
Associativity of Binary Operations
Distributivity applies when multiplication performed on
a group of two numbers added or subtracted together.
Example:
𝟐 𝟑 + 𝟒 = 𝟐 𝟑 + 𝟐(𝟒)
An element 𝑒 is said to be an identity element (or neutral
element) of a binary operation if under the operation any
element combined with 𝑒 results in the same element
Therefore, the identity element 𝑒 in addition is 0 and the
identity element 𝑒 in multiplication is 1.
Identity Elements of Binary Operations
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.
Therefore, the inverse element of addition is the
− 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 and the element of multiplication is
𝑡ℎ𝑒 𝑟𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟.
Inverses of Binary Operations
an instrument for
appraising the correctness of
reasoning.
Logic
is a declarative statement that is
true or false but not both.
A proposition P
A word or symbol that joins
two sentences to produce a
new one
LOGICAL
CONNECTIVES
a table that shows the truth value of a
compound statement for all possible truth values of its simple statements.
TRUTH TABLE
