Test the following syllogisms to determine which are valid and which are invalid. Translate them into standard form categorical claims, putting brackets around the terms, then apply each test, telling which ones it passes.
1. All halyards are lines that attach to sails. Painters do not attach to sails, so they must not be halyards.
2. No blank disks contain any data, although some blank disks are formatted. Therefore, some formatted disks do not contain any data.
3. All tobacco products are damaging to people's health, but some of them are addictive substances. Some addictive substances, therefore, are damaging to people's health.
4. No argument with false premises is sound, but some of them are valid. So, some valid arguments are not sound.
5. All clothes made from cotton are clothes that shrink. All clothes that shrink are clothes that are too big in the store. So, no clothes that are too big in the store are clothes made from cotton.
6. Every time Louis is tired, he's edgy. He's edgy today, so he must be tired today.
7. All citizens are residents, and all voters are citizens. So no residents must be voters.
8. Only people who hold stock in the company may vote, so Mr. Hansen must not hold any stock in the company, because I know he was not allowed to vote.
Answers
1.
All H are S.
No P are S.
So, no P are H. Valid
2.
No BD are DD.
Some BD are FD.
Therefore, some FD are not DD. Valid.
3.
All TP are DPH.
Some TP are AS.
Therefore, some AS are DPH. Valid
4.
No AFP are SA.
Some AFP are VA.
So, some VA are not SA. Valid
5.
All CC are S.
All S are TBS.
So, no TBS are CC. Invalid
6.
All TLT are TLE.
All TODAY are TLE.
So, all TODAY are TLT. Invalid(Louis could be edgy today for a different reason.)
7.
All C are R.
All V are C.
So, no R are V. Invalid
8.
All PWV are PSC. (PSC goes into the predicate slot because it is preceded by "only."
No MH are PWV. (This is a premise, even though it comes at the end.
So, no MH are PSC. (This is the conclusion, indicated by "so.") Invalid
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