$∀$ , For All, Conjunction, ∧, all things $∃$, Exist, Disjunction, ∨, at least one
$∃x$[$A(x) ∧ B(x)$] ≠ $∃x$$A(x)$ ∧ $∃x$$B(x)$, False
There is a game player who is both an attacker and a defender.
There is a game player who is an attacker, and There is a game player(another one?) who is a defender.
$∃x$[$A(x) ∨ B(x)$] = $∃x$$A(x)$ ∨ $∃x$$B(x)$
There is a game player who is an attacker or a defender.
There is a game player who is an attacker, or who is a defender.
$∀x$[$A(x) ∨ B(x)$] ≠ $∀x$$A(x)$ ∨ $∀x$$B(x)$, False
All nature number are even or odd
All nature number are even, or All nature number are odd
$∀x$[$A(x) ∧ B(x)$] = $∀x$$A(x)$ ∧ $∀x$$B(x)$
All athletes are both strong and big