Beginning Algebra Contents
Sets
Definition of a set and notation
Set membership
Set builder notation
Cardinal number
Ordinal number
Equal sets
Subsets
The empty set or the null set
Universal set or universe
Power set
Operations on Sets and Venn Diagrams
Union, intersection and difference
Partition of a set
The fundamental laws of the algebra of sets
Sets and Logic
The "and", the conjunction or the logical product
The "or", the disjunction or the logical sum
Logical negation
Relations
The Cartesian product
The domain and the range
Function
Relation on a set
Reflexive, symmetric, transitive and equivalent relation
Boolean Algebra
Definition
Basic theorems
Boolean operations on sets
Logic Gates and Circuits
The "AND" gate, the "OR" gate and the "NOT" gate
Binary Numbers System
Binary to decimal conversion
Decimal to binary conversion
Binary addition
The half adder
The Binary addition circuit - the full adder
Binary subtraction
The method of subtraction by adding the complement of the subtrahend applied to decimals
The method of subtraction by adding the complement of the subtrahend applied to binary numbers
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