SOLUTION: Determine which, if any, of the three statements are equivalent. I) If there is no food left on the table, then we have had dinner. II) If we have had dinner, then there is no fo

Question 294029: Determine which, if any, of the three statements are equivalent.
I) If there is no food left on the table, then we have had dinner.
II) If we have had dinner, then there is no food left on the table.
III) If there is food left on the table, then we have not had dinner.

I, II, and III are equivalent
I and II are equivalent
II and III are equivalent
I and III are equivalent
None are equivalent

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Contrapositives are equivalent.
Switch the arguments and negate both
I If there is no food left on the table, then we have had dinner.
.....If we have not had dinner, then there is food left on the table
II) If we have had dinner, then there is no food left on the table.
III) If there is food left on the table, then we have not had dinner.
II and III are contrapositives and are equivalent.
This was also answered in January
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.263278.html
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