Cheatography

# Math 1901 Final Cheat Sheet by SirUmbreon77

### 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}

### 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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