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Math 381
Test 2
15
Mathematics
Undergraduate 3
03/24/2009

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Term
set
Definition
collection of objects in which the ordering is not important and we won't consider repeated elements as being distinct from one another
Term
cardinality
Definition
the number of elements in A (size). |A|
Term
subset
Definition
is a set AND every element in the subset is also an element of the original set
Term
power set
Definition
the power set of S is the set of all subsets of the set S. They have to be 2^n
Term
symmetric difference
Definition
elements that are in either A or B but not in both.
Term
A-B
Definition
elemets that are in A but not in B
Term
AXB
Definition
{(a,b)| a in A ^b in B}
Term
injective
Definition
f:A-->B is injective (one-to-one) provided each x gets exactly one y AND each y gets exactly one x
Term
surjective
Definition
f:A-->B is called surjective ("onto") provided each element in the co-domain B has a pre-image element in the domain.. there's a least one x for each y
Term
relatively prime
Definition
the gcd is 1
Term
Given gcd(a,b)=d, then the equation ax+by=w has integer solutions x,y iff..
Definition
d|w
Term
the inverse (x^-1) of x in mod n
Definition
x*y=1 mod n
Term
in modn with n>2, an element is invertible iff
Definition
a,n are relatively prime
Term
|A n B| =
Definition
|A| + |B| -|A U B|
Term
bijective
Definition
a function which is both injective and surjective
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