Math (Sets)
What is Demorgan's law?
(AUB)^1 = A^1 n B^1 & (AnB)^1 = A^1 U B ^1
2^n
The # of subsets
What are inequalities?
If A & B are finite sets, A has fewer elements than B.
What is a subset? and whats the symbol?
A is a subset of B which means every element in A is also in B. The symbol is similar to and equal or greater than sign but its circular
what is the definiton of equal sets
every element in A is also in B, every element in B is also in A. Equal sets have the same elements, not necessarily in same order. A=B
what s a proper subset?
A is a proper subset of B means that every element in A is also in B. But there is at least 1 element in B not in A. The symbol is a sideways C
What is the infinite set?
A set put into a 1 to 1 correspondence with a proper subset of itself.
Distributive Laws
AN(BUC) = (AnB)U(ANC) & AU(BnC) = (AUB)n (AUC)
Commutative Laws
AnB= bnA & AUB = BUA
What is equivalent sets?
Can be put into a 1 to 1 correspondence with each other. A (squiggle sign) B. They have the same # of elements.
what is a 1 to 1 correspondence?
If the elements of set A and set B can be paired so that for each element of A there is exactly one element of B
What is the universe?
The set of all #'s under consideration. Symbol equals U
What is a set union?
The set of all x such that x belongs to A or B or both. {XlX E A or X E B or X E both A & B)
What is the difference of sets?
The set of all x such that x belongs to a and x doesnt belong to b. A-B = { X l X E A and X (crossed E) B}
A^ 1 ( What is the compliment of A)
The set of all x such that x belongs to the universe and x doesnt belong to A { X l X E U and X E A}
what is Cartesian Product of Sets?
The set of ordered pairs (x,y) such that x belongs to set A and y belongs to set B. AXB = { (x,y) l X E A and Y EB}
What is disjoint?
What a question is equal to nothing
how can you show the empty set?
a circle with a line through it or empty brackets
what is a set?
a collection of objects (well defined) called elements
what is set theory?
the basis of all mathematics
N(A) = ?
the number of elements in set A , the cardinal number
What is set intersection?
the set of all x such that x belongs to A and x belongs to B. AnB = { X l X E and X E B }
What is an ordered pair
(a,b) a is the 1st component b is the 2nd. (a,b) not equaled to (b,a)
A set can be defined by what 3 ways?
1.) by giving a verbal description 2.) by listing. 3.) by using set builder notation
What is Associative Laws?
An(BnC) = (AnB)nC & AU(BUC) = (AUB)UC
If 2 equal sets are equivalent the.. 2 equivalent sets...
may not be equal
