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## Here's the Solution to this Question

### Solution:

1. Origin Statement: "Some dogs can learn new tricks."

In symbols: $\exist x\in Dogs\, \, Can(x,LearnTricks)$

Negation: $\forall x\in Dogs\, \, \neg Can(x,LearnTricks)$

in English: "No dog can learn new tricks."

2. Origin Statement: "No rabbit knows calculus."

In symbols: $\forall x\in Rabbits\, \neg Knows(x,Calculus)$

Negation: $\exist x\in Rabbits\, Knows(x,Calculus)$

in English: "Some rabbits know calculus."

3. Origin Statement: "Every bird can fly."

In symbols: $\forall x\in Birds\,\, Can(x,Fly)$

Negation: $\exist x\in Birds\, \neg Can(x,Fly)$

in English: "Some birds can not fly."

4. Origin Statement: "There is no dog that can talk."

In symbols: $\neg(\exist x\in Dogs\, Can(x,Talk))$ or $\forall x\in Dogs\, \neg Can(x,Talk)$

Negation: $\exist x\in Dogs\, Can(x,Talk)$

in English: "There exists dog that can talk."

5. Origin Statement: "There is no one in this tutorial who knows French and Russian."

In symbols: $\neg(\exist x\in Tutorial\, Knows(x,French)\wedge Knows(x,Russian))$ or $\forall x\in Tutorial\, \neg Knows(x,French)\vee \neg Knows(x,Russian)$

Negation: $\exist x\in Tutorial\, Knows(x,French)\wedge Knows(x,Russian)$

in English: "Someone in this tutorial knows French and Russian."