I am doing a class on logic and I was given the following question: Is this predicate a valid formalization of "some dogs are sleepy"?
The statement in question is
$\exists d \in Dogs: is\,a \,dog(d) \implies sleepy(d)$
now I know that the rule of thumb is that we should use the conjunction. My understanding of the question was that $is\,a\,dog(d)$ is a tautology based on the previous predicate bounding $d$ to $Dogs$. This would result in the following predicate:
$\exists d \in Dogs: True \implies sleepy(d)$
then this would be equivalent to:
$\exists d \in Dogs: sleepy(d)$
giving interpreting the resulting predicates gives the meaning: "some dogs are sleepy". Can modus ponens be used in predicate to infer that two predicates are equivalent, thus giving them the same meaning?