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dog(x) = x is a dog

Int (x) = x is intelligent

write in logic form

No dogs are intelligent.
in Mathematical Logic by Junior (923 points) | 56 views

1 Answer

+3 votes

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 $\forall x( \sim Int(x))$

by Boss (27.5k points)

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