Rule number #1 says that there needs to be a sufficient and necessary condition. That checks out.
Rule number two says that the sufficient variables need to match in order to come up with a valid conclusion.
In this example, that is not the chase. Rule Number #2 does not check out. And the the criteria for Rule number #1's exception does not check out.
With all that being said, why is the answer not "No Valid Conclusion?" I was able to force the equation to come up with the what is listed as the correct answer, but it appears, based on the lecture, that doing so violates the criteria.
Please explain. Thanks!
Replies
Create a free account to read and
take part in forum discussions.
@Brenton your interpretation of rule 2 here is incorrect.
Ask yourself, what variable do these two statements share in common?
The answer is B.
You are correct, however, that currently our sufficient & necessary principle has "not B" but we convert this to "B" by writing out the contrapositive:
B ==> X
Before we can combine this with our quantifier statement, we are going to have to reverse our quantifier as follows:
S-some-B
We can now combine with our sufficient & necessary principle:
S-some-B ==> X
Which allows us to conclude:
S-some-X X-some-S
So (A) would be the correct answer.
Hope that helps! For a more detailed discussion of these concepts, please watch our video lesson on Quantifiers.
BrentonSeptember 8, 2016
That makes sense. I guess I just didn't realize that we had the freedom to use a contrapositive to tie one statement to a quantifier statement which has been converted to some then reversed. Individually each rule makes sense, just applying those several steps almost felt like "forcing" it to work, if you know what I mean. Thanks!
