Answer :
Final answer:
The argument is valid because, based on the premises, there are short poems that are not sonnets. Since all haikus are short poems and haikus are not sonnets, it logically follows that some short poems must be excluded from the sonnet category. Thus, the conclusions drawn from the premises hold true.
Explanation:
Validity of the Argument
To determine whether the argument is valid or invalid, we first need to analyze its premises and conclusion:
- Premise 1: All haiku are short poems.
- Premise 2: No haiku are sonnets.
- Conclusion: Hence, some short poems are not sonnets.
We can represent the premises as follows:
- Let H = set of haiku
- S = set of sonnets
- P = set of short poems
From Premise 1, we have: H ⊆ P, which means that all haikus fall within the category of short poems. From Premise 2, we have: H ∩ S = ∅, meaning haikus and sonnets do not overlap at all.
By the principles of logic, if all haikus are categorized as short poems and none of them are sonnets, then it follows that some short poems (specifically those outside of haikus) could indeed be sonnets or be other types of poems that are not sonnets. Therefore, we can conclude that:
The conclusion is valid, as it correctly deduces that based on the premises, there are indeed some short poems (such as those not classified as haiku) that are not sonnets.
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