Science:Math Exam Resources/Courses/MATH220/April 2005/Question 02
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Question 02 

Consider the following two statements: One of the statement is true, and the other is false. Determine which is which. For the true one, prove that it is true; for the false one, prove that it is false. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Try reformulating these two statements into more readable English. 
Hint 2 

The first statement is equivalent to

Hint 3 

The second statement is equivalent to

Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The second statement should appear wrong fairly immediately since it talking about the existence of the smallest real number which cannot exist. Let's prove this:
Now we can prove that the first statement is true:
