Science:Math Exam Resources/Courses/MATH220/December 2009/Question 02 (a)
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Question 02 (a) 

Write the negation of the following statement: 
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 

Remember that bringing negations across for all statements changes them to exists statements and vice versa. 
Hint 2 

Remember that (if A then B) is logically equivalent to 
Hint 3 

Remember that (The left and right hand sides above are logically equivalent) 
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. Following the hints, first rewrite the original using hint 3 as Now, taking the negation: Bring the negative in one level: Distribute across the bracket using the hints: Bring the negative inside: 