Lesson 2 Flashcards
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 โ 3 = 3 โ 2
Commutativity of Binary Operations
A binary operation is said to be associative if parentheses
can be reordered and the result is equivalent.
Example:
๐ + ๐ + ๐ = ๐ + ๐ + ๐
๐ โ ๐ โ ๐ = ๐ โ (๐ โ ๐)
Associativity of Binary Operations
Distributivity applies when multiplication performed on
a group of two numbers added or subtracted together.
Example:
๐ ๐ + ๐ = ๐ ๐ + ๐(๐)
An element ๐ is said to be an identity element (or neutral
element) of a binary operation if under the operation any
element combined with ๐ results in the same element
Therefore, the identity element ๐ in addition is 0 and the
identity element ๐ in multiplication is 1.
Identity Elements of Binary Operations
For an element ๐ฅ, the inverse denoted ๐ฅโ1 when combined with ๐ฅ under the binary operation results in the identity element for that binary operation.
Therefore, the inverse element of addition is the
โ ๐๐ ๐กโ๐ ๐๐ข๐๐๐๐ and the element of multiplication is
๐กโ๐ ๐๐๐๐๐๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐ข๐๐๐๐.
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
