math no2

Hierarchy of the number sets

N Z Q R

Is subset of

Countable sets

N Z Q

Uncountable sets

R and irrational numbers

Commutative law

Przemienność

The orders does not matter

Idempotent laws

Idempotencja

Overlapping a group with itself doesn't change anything (A and A is just A). 

Associative Laws

Łączność

When you have three or more groups, the way you group parentheses doesn't change the final outcome

Absorption Laws

(Prawa pochłaniania):

Combining a set with an intersection/union of itself and another set absorbs the secondary term

Distributive Laws

Dystrybutywność

Intersection distributes over union, and union distributes over intersection

A \cap (B \cup C) = (A \cap B) \cup (A \cap C)

De Morgan's Law

Prawa de Morgana:

The complement of a union is the intersection of the complements, and vice versa

Double Negation Double complement

Podwójna negoja

The complement of a complement returns the original set

Law of Excluded Middle & Non-Contradiction

Prawo niesprzeczność prawowyłączonego środka

A set combined with its complement yields the universal set, while their intersection yields the empty set

proposition sentence

Zdanie

Basic statements that are strictly either true or false. Instead of writing full sentences, we use shorthand letters like p, q, or r. 

Conjugations

koniunkcja /\

And

Disjunction

alternatywa / dysjunkcja \/

Or

Negation

negacja (buu shig ym)

Not

Implication

Implikacja →

If then

What are WFF

The "grammar rules" for writing logic statements so they actually make sense instead of being total gibberish

Rules of writing wff

Single letters (p, q, etc.) count as valid statements on their own, and you can build longer sentences by linking them with proper operators and parentheses.