SET THEORY
The set theory of sets lies at the foundation of mathematics. Concepts in set theory such as functions and relations appear explicitly or implicitly in every branch of mathematics. The fundamental concept of all branches of mathematics is that a set.
George Boole was born on November 2,1815. His father was a shopkeeper. He pointed out that there was a close relationship between symbols that represents logical instructions and algebraic symbols.Boole would be pleased to know that his Boolean algebra is the basis of all computer arithmetic.At the age of 24 George Boole published his first paper "Researches on the Theory of Analytical transformation" in the Cambridge mathematical journal.
The theory of sets as a mathematical discipline originated with the German mathematician George Cantor.George Cantor was born on March 3 , 1845.
Augustus De morgan was born in Madurai, Tamlinadu. His family move to England when he was seven months old. De morgan's laws the three basic set operations Union, Intersection and complement.
- Introduction to set
- Representation of sets
- Descriptive form of set
- Set builder form
- Roster form
- Types of sets
- Union of two set
- Intersection of sets
- Symmetric difference of two sets
- Complement of a set
- Difference of two sets
- Cardinal number of set
- Cardinal number of power set
- Subset of null set
- Proper subset of a set
- Cartesian product of two sets
- Number of proper subsets of a set
- Set operations
- Representation of set operations using venn diagram
- Venn diagram A U B
- Venn diagram A n B
- Venn diagram of A'
- Venn diagram of B'
- Venn diagram of (AUB)'
- Venn diagram of (AnB)'
- Venn diagram of A\B
- Venn diagram of B\A
- Symbols used in set theory
- Formulas used in set operations
- Properties of set operations
- Commutative property of set
- Associative property of set
- Distributive property of set
- De morgans's law for set difference
- De morgan's law for compliments
- Venn diagram word problem with 3 circles
- Formula for (A U B U C)
- How do you figure out if a relation is a function
- How do you figure out if a relation is a function
- Representation of functions
- Vertical line test
- Types of functions
- How to find inverse of a function
- How to find inverse of a function using composition
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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
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