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24 Cards in this Set
- Front
- Back
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Definition of a set |
A set is a collection of well-defined objects/elements |
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What is the cardinality of A? How is this written? |
The number of elements in A. It's written as #(set) = an integer greater than or equal to 0 |
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Cardinality of the empty set |
0 |
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What does it mean when A is a subset of B? |
Everything in A is in B |
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What does it mean when A is a proper subset of B? |
Everything in A is in B, but A is not equal to B |
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What is the powerset of A? |
The set of all subsets of A |
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If #(A) = n then what is #(P(A))? |
#(P(A)) = 2^n |
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Define A compliment |
Everything NOT in A |
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Define A union B |
Everything in A or B |
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Define intersection of A and B |
Everything in A and B |
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Use deMorgons law to rewrite (A U B)^c |
A^c intersect B^c |
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Use deMorgons laws to rewrite (A intersect B)^c |
A^c U B^c |
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When are unions and intersections associative? |
When you have all unions or all intersections, no mixes of the two |
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Distribute (A intersect B) U C |
(A U C) intersect (B U C) |
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Distribute (A U B) intersect C |
(A intersect C) U (B intersect C) |
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#(AUB) = |
#(A) + #(B) - #(A intersect B) |
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#(AUBUC) = |
#(A) + #(B) + #(C) -#(AintB) -#(AintC) -#(BintC) +#(AintBintC) |
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Formula for nPk = |
(n)(n-1)(n-2)....(n-k+1) Or N factorial up to k |
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Does order matter for nPk or nCk? |
nPk |
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Formula for nCk = |
n!/[(k!)(n-k)!] |
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What does it mean when two sets are disjoint? |
Their intersection is the empty set |
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P(E) = |
#E/#S |
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P(F|E) = |
[P(E intersect F)/P(E) |
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When can we use P(F|E) = [#(E int F)]/[#(E)] |
If and only if all outcomes are equally likely |
