Identify what you can properly conclude from the given premises:
P: D → not AP: X–some–AC: ?
pleaseandthankyouMay 23, 2016
Need further help breaking this down
I'm having some trouble understanding the explanations of these particular types of questions, normally just because they're in an abbreviation style I'm unaccustomed to.
Can you please help to explain the correct answer and how we arrive at x-some-A-not-D? I'm not following.
Thanks!
Replies
Create a free account to read and
take part in forum discussions.
To make a valid deduction with a Quantifier Statement and a Sufficient & Necessary statement, the variable the statements have in common must be the sufficient condition in the Sufficient & Necessary condition.
Our two premises here are:
P: D ==> not A
P: X-some-A
What variable do these share in common? A.
Is A the sufficient condition? Yes! The contrapositive of our first premise is A ==> not D.
So we can combine these statements to make a valid deduction as follows:
X-some-A ==> not D
To conclude:
X-some-not D
This must be true. If some Xs are As, this means at least one X is a A.
And since no A is a D, we know that at least one X is also not a D.
Hope this helps! For a more in-depth review of these concepts, check out our lesson on Quantifiers.
