cw916
contestada

Which of the following has no solution?

{x | x ≤ 1} and {x | x ≥ 1}
{x | x < 1} and {x | x > 1}
{x | x ≤ 1} or {x | x ≥ 1}

Respuesta :

a)

[tex]\{x\,|\,x \leq 1\}\, \cap \,\{x\,|\,x \geq 1\}=(-\infty;1]\,\cap\,[1,\infty)=\{1\}[/tex]

b)

[tex]\{x\,|\,x \ \textless \ 1\}\, \cap \,\{x\,|\,x \ \textgreater \ 1\}=(-\infty;1)\,\cap\,(1,\infty)=\boxed{\emptyset}[/tex]

c)

[tex]\{x\,|\,x \leq 1\}\, \cup \,\{x\,|\,x \geq 1\}=(-\infty;1]\,\cup\,[1,\infty)=\mathbb{R} [/tex]

Answer b)