Science:Math Exam Resources/Courses/MATH220/December 2011/Question 03
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Question 03 

For statements P, Q and R, prove that the statement is a tautology. 
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 

Use the identity 
Hint 2 

Use the identity 
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. Using both hints, we can rewrite the statement into equivalent statements as follow The last equivalent statement is of the type A AND B with which both are tautologies since they contain P OR not P and respectively not Q OR Q. So if both A and B are tautologies, then so is the conjunction of them into the statement A AND B. 