gaokao 2015 Q4

gaokao · China · zhejiang-science Not Maths
4. The negation of the proposition ``$\forall n \in \mathbb{N} ^ { * } , f ( n ) \in \mathbb{N} ^ { * }$ and $f ( n ) \leq n$'' is
A. $\forall n \in \mathbb{N} ^ { * } , f ( n ) \in \mathbb{N} ^ { * }$ and $f ( n ) > n$
B. $\forall n \in \mathbb{N} ^ { * } , f ( n ) \in \mathbb{N} ^ { * }$ or $f ( n ) > n$
C. $\exists n _ { 0 } \in \mathbb{N} ^ { * } , f \left( n _ { 0 } \right) \in \mathbb{N} ^ { * }$ and $f \left( n _ { 0 } \right) > n _ { 0 }$
D. $\exists n _ { 0 } \in \mathbb{N} ^ { * } , f \left( n _ { 0 } \right) \notin \mathbb{N} ^ { * }$ or $f \left( n _ { 0 } \right) > n _ { 0 }$
4. The negation of the proposition ``$\forall n \in \mathbb{N} ^ { * } , f ( n ) \in \mathbb{N} ^ { * }$ and $f ( n ) \leq n$'' is\\
A. $\forall n \in \mathbb{N} ^ { * } , f ( n ) \in \mathbb{N} ^ { * }$ and $f ( n ) > n$\\
B. $\forall n \in \mathbb{N} ^ { * } , f ( n ) \in \mathbb{N} ^ { * }$ or $f ( n ) > n$\\
C. $\exists n _ { 0 } \in \mathbb{N} ^ { * } , f \left( n _ { 0 } \right) \in \mathbb{N} ^ { * }$ and $f \left( n _ { 0 } \right) > n _ { 0 }$\\
D. $\exists n _ { 0 } \in \mathbb{N} ^ { * } , f \left( n _ { 0 } \right) \notin \mathbb{N} ^ { * }$ or $f \left( n _ { 0 } \right) > n _ { 0 }$