Tag: Algebra PDF Books

Definitions: N : Natural numbers N0 : Whole numbers Z : Integers Z+ : Positive integers Z− : Negative integers Q : Rational numbers C : Complex numbers Formulas: Natural numbers (counting numbers ) N={1,2,3,…} Whole numbers ( counting numbers with zero ) N0={0,1,2,3,…} Integers ( whole numbers and their opposites and zero ) Z={…,−2,−1,0,1,2,…} Z+=N={1,2,…} Z−={…,−3,−2,−1} Z=Z−∪0∪Z Irrational numbers: Non repeating and nonterminating integers Real numbers: Union of rational and irrational numbers Complex numbers: C={x+iy | x∈R  and  y∈R} N⊂N0⊂Z⊂Q⊂R⊂C

Definitions: Universal set : I Empty set: ∅ Union of sets A∪B={x:x∈A  or  x∈B} Intersection of sets A∩B={x:x∈A  and  x∈B} Complement A′={x∈I:x∉A} Difference of sets A∖B={x:x∈A  and  x∉B} Cartesian product A×B={(x,y):x∈A  and  y∈B} Set identities involving union Commutativity A∪B=B∪A Associativity A∪(B∪C)=(A∪B)∪C Idempotency A∪A=A Set identities involving intersection Commutativity A∩B=B∩A Associativity A∩(B∩C)=(A∩B)∩C Idempotency A∩A=A Set identities involving union and intersection Distributivity A∪(B∩C)=(A∪B)∩(A∪C) A∩(B∪C)=(A∩B)∪(A∩C) Domination A∩∅=∅ A∪I=I Identity A∪∅=∅ A∩I=A Set identities involving union, intersection and complement Complement of intersection and union A∪A′=I A∩A′=∅ De Morgan’s laws (A∪B)′=A′∩B ′ (A∩B)′=A′∪B ′ Set identities involving difference B∖A=B∖(A∪B) B∖A=B∩A′ A∖A=∅ (A∖B)∩C=(A∩C)∖(B∩C) A′=I∖A