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Math 1901 Final Cheat Sheet by

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
Comp­lim­ent: the set consisting of all element in U that are not in A
Set builder notation
{formula for elements| restri­ctions}

Venn Diagrams

 

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

Negation

p
~p
T
F
F
T

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
 

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

Circuits

Logic Circuits

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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