Week 4 - The Prelude to Execution.

    A third of the semester has gone by and it is about time for the first term test. This week was for us to practise for the test by grinding through the dreadful assignment. To be honest, the assignment questions were not too much stress except a few particular. Along with my group, we were able to knock through most of the questions. However, we got stuck upon the venn diagrams drawing of question four. It was difficult to imagine the diagrams through our minds. Therefore, we constructed a truth table and drew accordingly to table. However, the quantifiers further confused us as difference orders of the quantifiers affect the meaning of statement. Simply by switching the order of the quantifiers can alter the truth of the statement.

For example:  Let N and M = {1, 2, 3, 4,}


For all of the x in N,  there exists a y in M such that x + y = 5
    This statement will always be true.


However...
If we switch the order of quantifier...


There exists a y in M, such that for all x in N, x + y = 5
    This statement will return a false since there is a counter example which depict that x + y != 5

Nevertheless, there are double quantifiers which allows for unsorted order of quantifiers; the order of the quantifiers will not result in the change of the truth.

To sum up the week, we were introduced the basic structure of the proof. The structure was hard to followed in the first place since I used to do math questions in a rather not organized fashion. However, through some practise, I was able to grasp the fundamentals of proof structure and is able to twist myself to think more logically, constantly providing evidence and reasoning in my operations.