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1. If the Domain is All the animals.

No dogs are intelligent = $\sim \exists x (Dog(x) \wedge Int(x) )  $

Interpretation : There does not exists any animal which is Both Dog and intelligent.

Or 

$\forall x(Dog(x) \rightarrow \,\,\sim Int(x))$

Interpretation : For all animals, If It is Dog then It is Not intelligent.

2. If the Domain is All Dogs : 

(Just make the Dog(x) in the above formulas True(T)..)

Hence, 

No dogs are intelligent = $\sim \exists x ( Int(x) )  $

Or $\forall x( \sim Int(x))$

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Vegeta asked Jun 14, 2018
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P(x,y,z), xy=z, Universe is interger;write in logic formIf xy=x for all y, then x =0.Thank you