Short Inference Question

mac35352 · April 1, 2011, 2:23am

If we have that all Gs are Hs and some Hs are Is. Is there a connection between G and I?

incompetentia · April 1, 2011, 2:24am

no

dakatz · April 1, 2011, 2:30am

There is no deduction you can make from this. It is certainly possible for the statement to be true, but in no way is it guaranteed. I always find it smart to plug in actual factors instead of letters. This usually makes it clear whether or not an inference is erroneous or not.

Lets say all Californians are Americans, and some Americans are Texans.

This is the logical equivalent to your statement (though a bit different in that my hypothetical doesn’t technically allow any overlap between G and I, but I’m sure you get the point)

mac35352 · April 1, 2011, 2:34am

Thanks for the example. It’s better to see it that way. What if I had a most instead of a some? Still can’t infer that (using your example). All Californians are Americans and most Americans are Texans? that still wouldn’t yield any inferences.
Correct?

dakatz · April 1, 2011, 2:37am

Nope, still no deduction. Here is a more clear example using the exact same logic. Again, I’m all about using real-world examples that intuitively make sense (and obviously most Americans are not Texans in real life)

All Alaskans are Americans, and most Americans live in the continental US

Would there need to be any overlap between Alaskans and people who live in the continental US? No. Once again, this is a bit misleading because there CAN’T be overlap between the two groups, which isn’t a situation that arises if we are working with mere factors represented by letters.

mac35352 · April 1, 2011, 2:40am

dakatz:

mac35352:

Thanks for the example. It’s better to see it that way. What if I had a most instead of a some? Still can’t infer that (using your example). All Californians are Americans and most Americans are Texans? that still wouldn’t yield any inferences.
Correct?

Nope, still no deduction. Here is a more clear example using the exact same logic. Again, I’m all about using real-world examples that intuitively make sense (and obviously most Americans are not Texans in real life)

All Alaskans are Americans, and most Americans live in the continental US

Would there need to be any overlap between Alaskans and people who live in the continental US? No. Once again, this is a bit misleading because there CAN’T be overlap between the two groups, which isn’t a situation that arises if we are working with mere factors represented by letters.

So, we can’t infer that but it could be true. Because some Alaskans could live in continental US.

dakatz · April 1, 2011, 2:44am

mac35352:

dakatz:

mac35352:

Thanks for the example. It’s better to see it that way. What if I had a most instead of a some? Still can’t infer that (using your example). All Californians are Americans and most Americans are Texans? that still wouldn’t yield any inferences.
Correct?

Nope, still no deduction. Here is a more clear example using the exact same logic. Again, I’m all about using real-world examples that intuitively make sense (and obviously most Americans are not Texans in real life)

All Alaskans are Americans, and most Americans live in the continental US

Would there need to be any overlap between Alaskans and people who live in the continental US? No. Once again, this is a bit misleading because there CAN’T be overlap between the two groups, which isn’t a situation that arises if we are working with mere factors represented by letters.

So, we can’t infer that but it could be true. Because some Alaskans could live in continental US.

Right, all you can say is that it could possibly be true. If you have any other formal logic questions, shoot away. This was one of my favorite things about the test.

mac35352 · April 1, 2011, 2:47am

dakatz:

mac35352:

dakatz:

mac35352:

Thanks for the example. It’s better to see it that way. What if I had a most instead of a some? Still can’t infer that (using your example). All Californians are Americans and most Americans are Texans? that still wouldn’t yield any inferences.
Correct?

Nope, still no deduction. Here is a more clear example using the exact same logic. Again, I’m all about using real-world examples that intuitively make sense (and obviously most Americans are not Texans in real life)

All Alaskans are Americans, and most Americans live in the continental US

Would there need to be any overlap between Alaskans and people who live in the continental US? No. Once again, this is a bit misleading because there CAN’T be overlap between the two groups, which isn’t a situation that arises if we are working with mere factors represented by letters.

So, we can’t infer that but it could be true. Because some Alaskans could live in continental US.

Right, all you can say is that it could possibly be true. If you have any other formal logic questions, shoot away. This was one of my favorite things about the test.

Excellent. Thanks