Les propositions suivantes sont-elles vraies ou fausses ?
\((\exists a\in\mathbb R)(\exists b\in\mathbb R )[(a > 0~et~b > 0)~et~ab \leq 0]\)
\((\exists a\in\mathbb R )(\exists b\in\mathbb R )[ab > 0~et~(a \leq 0~ou~b \leq 0)]\)
\((\exists a\in\mathbb R )(\exists b\in\mathbb R )[ab > 0~et~(a \geq 0~ou~b \geq 0)]\)
\((\exists a\in\mathbb R )(\exists b\in\mathbb R )[(a < 0~et~b < 0)~et~ab \leq 0]\)