Mệnh đề nào dưới đây đúng:

\[\left( {\forall {\rm{x}} \in \left[ {{\rm{a,b}}} \right]} \right){\rm{f(x)}} \ge 0{\rm{\& }}\exists {{\rm{x}}_0} \in \left[ {{\rm{a,b}}} \right]{\rm{f(}}{{\rm{x}}_{\rm{0}}}) > 0 \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(x)dx}} \ge 0\]

\[\exists {{\rm{x}}_0} \in \left[ {{\rm{a,b}}} \right]{\rm{:f(}}{{\rm{x}}_{\rm{0}}}) > 0 \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(x)dx}} > 0\]

\[\left( {\forall {\rm{x}} \in \left[ {{\rm{a,b}}} \right]} \right){\rm{f(x)}} \ge 0{\rm{\& }}\exists {{\rm{x}}_0} \in \left[ {{\rm{a,b}}} \right]{\rm{f(}}{{\rm{x}}_{\rm{0}}}) > 0 \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(x)dx}} > 0\]

\[\left( {\forall {\rm{x}} \in \left[ {{\rm{a,b}}} \right]} \right){\rm{f(x)}} \ge 0\]