Science:Math Exam Resources/Courses/MATH220/April 2011/Question 04
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Question 04 

Prove that

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 truth tables. Also, remember that is always true if P is false. 
Hint 2 

For another solution, do you know or can you prove that 
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 1  

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Using truth tables. We write the truth table for each of the two statements that we would like to compare.
And

Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Another solution consists of using an equivalent statement for the implication: So the statement becomes To prove this statement, we'll just show that the left hand side (LHS) is equal to the right hand side (RHS). For the LHS, we get since disjunction (the logical OR) is associative (that means doesn't care about brackets). For the RHS we get since again the disjunction is associative and having twice the ¬P term is useless. We obtained that LHS = RHS which proves the statement. 