Mathematical Thinking Stanford, W4

Quantifier(logic)

$∀$ , 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

All athletes are strong, and all athletes are big.