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Connie-TichoJuly 14, 2020
Diagraming B
Hi I was confused a little by diagramming the second premise in answer B. I think the word no throws me off with kn[owing what is sufficient and necessary.
Can you help clarify this for me?
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Thanks for the question! Yes, diagramming “no” statements is tricky at first, but let me try to help explain.
In general, when we diagram “No X are Y,” we diagram it as the following
X —> ~Y
And so in this case, when we’re told that no abstract painting will be included in next week’s art auction, we diagram it
Abstract painting —> ~Included in next week’s art auction
Now why does this make sense? Well, what does it mean to say that No X are Y? Let’s take an example: no turtles are mammals. Well, how can we phrase this in “if-then” language? It means that if an animal is a turtle, it’s not a mammal. Because no turtles are mammals! And we know how to diagram a statement like “if it’s a turtle, it’s not a mammal.” That’s just
Turtle —> ~Mammal
And again, that’s how we would diagram “No turtles are mammals.” So when we have “No X are Y,” we can take X, put it in the sufficient, and take Y, negate it, and put it in the necessary. Of course, you could also do the contrapositive
Y —> ~X
Which you could think of as (going back to the turtle example) “if something’s a mammal, then it’s not a turtle.” So really, you can take either term, put it in the sufficient, take the other, negate it, and put it in the necessary. They’re logically equivalent, so either way is fine; whatever makes most sense in your head.
Hope this helps! Feel free to ask any other questions that you might have.
