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CHAPTER 1 Sets, Proof Templates, and Induction
1.12.1 Terms, Theorems, Algorithms, and Templates
1.1 Summary
TERMS
algebraic identity
is a member of
real numbers
empty set
is an element of
set
equal
is contained in
set-theoretic notation
factor
is in
subset
finite set
is not an element of
universal set
if and only if
natural numbers
universe
implication
not finite sets
vacuously
infinite set
proper subset
Venn diagram
integers
rational number
THEOREM
A = B if and only if A C B and B C A
TEMPLATES
Template 1.1 Element Membership in a Set Template 1.5 Set Equality
Template 1.2 Set Inclusion
Template 1.6 Set Inequality
Template 1.3 Set Non-Inclusion
Template 1.7 Implications and If and Only If
Template 1.4 Proper Set Inclusion
1.3 Summary
TERMS
absolute difference
disjoint sets
minimum element
analogous
distributive lattice
power set
bit representation
equivalent statements
product
boolean algebra
inclusive or
proof by cases
bottom
indirect proof
relative difference
complement
intersection (n)
set difference
complementation
inverse
statement
complemented lattice
join (v)
symmetric difference
contrapositive
lattice
top
converse
maximum element
union (U)
counterexample
meet (A)
THEOREMS
Absorption Law for Join
Commutative Law for Intersection
Absorption Law for Meet
Commutative Law for Join
An Absorption Law
Commutative Law for Meet
Associative Law for Intersection
Commutative Law for Union
Associative Law for Join
DeMorgan's Law for Intersection
Associative Law for Meet
DeMorgan's Law for Union
Associative Law for Union
DeMorgan's Laws