Math (Sets)

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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


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