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Hi, I'm working on PS's section on formal logic and there is one problem that I don't quite understand:

E <--|--> F --> G --> H

I understand why F --> H and G some E are inferences, but the answer key also includes H some E. I'm not sure how this inference can be made since it shouldn't be able to go against the arrow, even with the inherent inference (H some G).

spets wrote:Hi, I'm working on PS's section on formal logic and there is one problem that I don't quite understand:

E <--|--> F --> G --> H

I understand why F --> H and G some E are inferences, but the answer key also includes H some E. I'm not sure how this inference can be made since it shouldn't be able to go against the arrow, even with the inherent inference (H some G).

You have to combine inferences, I think. I'm a bit rusty at this, but let me give it a shit.

F--->H (All F's are H)
+
F<--/-->E (No F's are E)

= (well if All F's are H, and No F's are E, some H's can't be E's)

H <some / > E (some H's can't be E's)

Apologies if this is incorrect, like I said i'm super rusty and am in need of a formal logic review.

Knockglock wrote:

spets wrote:Hi, I'm working on PS's section on formal logic and there is one problem that I don't quite understand:

E <--|--> F --> G --> H

I understand why F --> H and G some E are inferences, but the answer key also includes H some E. I'm not sure how this inference can be made since it shouldn't be able to go against the arrow, even with the inherent inference (H some G).

You have to combine inferences, I think. I'm a bit rusty at this, but let me give it a shit.

F--->H (All F's are H)
+
F<--/-->E (No F's are E)

= (well if All F's are H, and No F's are E, some H's can't be E's)

H <some / > E (some H's can't be E's)

Apologies if this is incorrect, like I said i'm super rusty and am in need of a formal logic review.

lolz for bold

Knock is correct. Maybe draw a venn diagram. F is contained by G which is contained by H. The E group does not overlap with F at all, so no matter how you draw it while abiding by these rules, you will have some H's that are not E's (namely, those H's that are in the subgroup G and the subgroup F). This is true even if you make the entire group of G and H into E's while omitting F's.

I did a very half ass job drawing it, note the bottom red does overlap with the F a little bit but meh, like I said, half-assed.