Final answer:
The negations for the statement "all dogs are loyal" are "There is a dog that is disloyal" and "Some dogs are disloyal". These contradictory statements indicate that not all dogs are loyal, thus negating the original claim.
Step-by-step explanation:
The question asks us to identify the negation of the statement "all dogs are loyal." A negation of a statement is its logical opposite — what would make the original statement false. Therefore, the following are negations:
Option (a) "There is a dog that is disloyal" suggests that at least one dog is not loyal, which counters the claim that all dogs are loyal. Option (f) "Some dogs are disloyal" also indicates that not all dogs are loyal, thereby negating the original statement.
Options b, c, d, and e are not correct negations of the statement "all dogs are loyal," because they either state something about animals other than dogs or imply a different meaning that does not directly contradict the original statement.