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# Question: if-then conditional statements

Alum Member
in General 199 karma
Using a kaplan book in conjunction with these videos and can use some help! Can anyone explain Kaplan's answer for the part B? I could have sworn it was an error.

A. What do we know if megan buys a juicer?
My answer: she bought mangos, kale, or both.
B. What do we know if megan buys neither mangos nor kale?
My answer: nothing. I thought that no logical deductions could be made from this statement because this is the necessary condition not the sufficient condition.
Kaplans answer: then she can't have bought a juicer
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• #### conditional chain linkage with "if but only if"/double arrowHi guys, So I know that for example A ---> B <--|--> C leads to the inference A <--|--> C, whereas A <--|--> B ---- > C leads to no useful inferen…

• Inactive ⭐
2116 karma
Answer B is the contrapositive of the statement:

When you take the contrapositive, you negate and switch "or" to "and". So if Megan does not buy kale "AND" mango, then Megan did not buy the juicer.
• Alum Member
199 karma
Ok that makes sense! Thanks a lot
• Inactive ⭐
2116 karma
No problem. Another way to simplify that argument is
J-> K or M

contra: notK and notM -> notJ
• Alum Member Inactive ⭐
edited April 2015 812 karma
@"Aiesha G." I would review JY's lessons on logic. This is what is called demorgan's law. You can deduce she did not buy a juicer.

http://7sage.com/lesson/contrapositives-demorgans-law/