What is the difference between Not all Y's are Z's and Not all Z's are Y's? Isn't the conclusion a some quantifier and the correct answer - Not all Z's are Y's - mean the same as Not all Y's are Z's since the conclusion is reversible?
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The statement "not all Y's are Z's" means that some Y's are not Z's. This is diagrammed as: Y - some - not Z. The reverse of this is: not Z - some - Y.
The statement "not all Z's are Y's" means that some Z's are not Y's. This is diagrammed as Z - some - not Y. The reverse of this is: not Y - some - Z.
Do you see the difference? While you are correct that some statements are reversible, these statements are using different variables and therefore make different conclusions.
Does that make sense? Please let us know if you have any other questions!
ajsFebruary 13, 2020
This makes sense. Thank you!
RaviFebruary 13, 2020
@ajs, let us know if you have any other questions!
