Cheatography
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Sets
∈ |
"Is an element of..." |
∪ |
Union: combine elements of A and B |
∩ |
Intersection: elements that appear in both sets |
⊄ |
Is not a subset of |
⊆ |
Subset: all elements in A are in B |
⊂ |
Proper Subset: A is a proper subset of B iff A is a subset of B and B is not equal to A |
∅ |
Empty set |
{ } |
Empty set |
{∅}
|
Not an empty set |
A̅ |
Compliment: the set consisting of all element in U that are not in A |
Set builder notation |
{formula for elements| restrictions} |
|
|
Conjunction
p |
q |
p∧ q |
T |
T |
T |
T |
F |
F |
F |
T |
F |
F |
F |
F |
Disjunction
p |
q |
pVq |
T |
T |
T |
T |
F |
T |
F |
T |
T |
F |
F |
F |
Other Statements
NAND |
Not And: Negation of And |
NOR |
Not Or: Negation of OR |
EOR |
Exclusive Or: exactly one of p and q is true |
Conditional Statement → |
If p then q |
Biconditional Statement ↔ |
p iff (if and only if) q |
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Boolean Tables
A |
B |
A + B |
A x B |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
Probability/Stats
Perms |
P(n,r) = n!/((n−r)!) |
Combs |
C(n,r) = n!/(n−r)!r! |
Sample Space |
Set of all possible outcomes |
Mean |
Sum of set divided by length of set |
Median |
Middle term of an organized |
| |
Take the average of two terms if there is more than one middle term |
Mode |
The number that occurs most in a set |
σ² (Variance) |
Calculate the mean For each number, subtract the mean and square the result Calculate the average of the squared differences, or sum up the squared differences and divide by N, the number of values. |
σ (Standard Deviation) |
Square Root of Variance (σ²) |
Probability Formulas
b= Binomial Probability |
b(x; n, P) = nCx Px (1 - P) |
n= number of trials |
x= number of successes |
P= probability of success |
Binomial Distribution |
μ = n·P |
| |
σ² = n · P · (1-P) |
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