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