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Modifiers in Conditional Statements

Chicago_HornChicago_Horn Alum Member
in Logical Reasoning 68 karma

If you have two separate conditionals both with the same suf or nec condition, but the modifiers for the suf or nec condition are different in each sentence, are the statement letters the same?

All cats which are furry and cute eat dogs
C->D
All cats which are bald and ugly eat dogs.
C->D or should it be C'->D

Alternatively, are "furry and cute" and "bald and ugly" simply subsets of cats? Does the necessary condition of D have two different sufficient conditions in this context?

Thank you!

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Comments

  • EveryCookCanGovernEveryCookCanGovern Alum Member
    401 karma

    Yes they are two separate sufficient conditions for the same necessary. If (cat) and (cute) and (furry) then (eats dogs). If (cat) and (bald) and (ugly) then (eats dogs). If (not eat dogs) then (not cat) or (not cute) or (not furry) and (not cat) or (not bald) or (not ugly).

  • LogicianLogician Alum Member Sage ⭐
    2464 karma

    Both sets of cats “furry and cute” and “bald and ugly” are subsumed in the group of all cats. In other words they would be classified as “some” cats. However, we don’t know if there’s an intersection between the two. Based on this they would both have to be classified separately (individual sufficient each) unless it so happens to be that they comprise the same exact group. I.e the same 50 that are furry and cute are also the same 50 that are bald and ugly- Which would be unlikely in this scenario lol. Anyways hope that helps!

  • lexxx745lexxx745 Alum Member Sage ⭐
    3190 karma

    Yep. They are different sufficient conditions.

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