Thursday, 25 September 2014

A Confused Question

Here is a confused question.


Which of the following statements are equivalent to the statement, “No two students in this class are not on fire.”? Which are equivalent to its negation? Which ones are neither?
(a)  “All student in this class, except at most one, are on fire.”
(b)  “Two students in this class are on fire.”
(c)  “For any pair of students in this class, one of them is on fire.”
(d)  “At least two students in this class are not on fire.”
(e)  “Your TA has put all the students out.”
(f)  “If I choose two students in this class and one of them is not on fire, then the other one is on fire.” 

I had some difficulties to understand the statement “No two students in this class are not on fire.” I tried to translate it to quantifiers and symbols. But that still could't help me figure the question out. Then I asked my roommate and he told me a smart way to solve this problem.

We divided “No two students in this class are not on fire.” into two cases.
1. 0 or 1 student is not on fire.
2. 2 or 3 or more student is on fire.

Now it is very clear and easy to determine which statements are equivalent, which are negations, and which are neither.




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