# Interpretation of symbols in logic and math

## Reading logic formulas

p → q

* if p then q
* given p, q
* p implies q
* q only if p
* q is the necessary condition for p
* p is a sufficient condition for q

if {it works} then {it'll revolve}

* given that it works, it's revolving
* it revolves only if it works _hmm_

p → ¬¬p

* if p, then it is NOT the case that NOT p

p ⇔ q

* p if and only if q
* if p then q and if q then p

(p = T) → (¬p = F) ∧ (¬¬p = T)\
if p is TRUE, then NOT p is FALSE and NOT NOT p is TRUE

p = ¬¬p

* if p is TRUE, then NOT NOT p is TRUE
* if p is FALSE, then NOT NOT p is FALSE

p = ¬¬p ¬¬q = q p ∧ q

p → q

* if p then q
  * if {it rains} then {the streets are wet}
* given p, then q
  * given {that n ∈ ℕ and even} then {n >= 0 and n ×÷⁒±‗ 2 = 0}
* p implies q
* q only if p
