In this
week of CSC165, I learned about conjunction, disjunction and negation. The conjunction and disjunction were very
similar to the ‘and (n)’ and ‘or (u)’ used in sets and Venn diagrams, and so it
was fairly easy for me to understand what they mean. Disjunction and conjunction are also
identical to the “and” and “or” commands in Python, which I had learned in
CSC108 already, so I was able to understand how they are used to evaluate
statements and implications. Basically, conjunction
is used when the conditions on either side of the sign must all be true in
order for the statement to be true. For
disjunction, only one of the condition being true will satisfy the requirement for
the statement as a whole to be true.
However, the use of brackets can modify which requirement comes first,
whether conjunction and disjunction, and during the tutorial this week I went
over some example statements that gave me a better grasp of how conjunction and
disjunction is used. To not be confused
by the order of the requirements, I like to underline parts of statements that
need to be considered first. For
example, if the statement was (P n Q) u R, I would draw a line under (P n Q),
and another under R, so I know which two objects I’m looking at and whether disjunction
or conjunction is the main requirement of the statement.
I also studied negation during in this week, and over
negation wasn’t a difficult concept to grasp.
It is basically the opposite of what is being said. That means if a statement is true, then its
negation is false. However, one problem I
tend to have when dealing with negation is that I often confuse them with
contrapositives. What I mean by this is
that when I try to find the negation of a statement, I end up finding the
contrapositive instead. To prevent this
problem from reoccurring repeatedly in the future, I realised that the negation
is the opposite of the statement, so if I put another negation sign in front of
the negated statement, then I would get the contrapositive.
Lastly, during the class on Friday I had the opportunity to
work with my friend on a problem which involves finding and expressing the
patterns of up and down creases of a paper strip folded n number of times. I devised a plan to first observe the first 4
folds and discover the basic relationships between the number of folds n, the
number of layers after being folded n times, and the number of creases c. We found that the number of creases can be
calculated using the formula 2^n – 1, which helps us understand how many
creases there are. However the problem
of how the pattern of ups and downs go still remain unsolved. We drew a diagram depicting the ups with
arrows pointing up, and downs with arrow pointing down, and discovered that
there exists a central crease which remains the same at all time. Every time the paper is folded, new creases
are generated on either side of existing creases, and the new creases have an
alternating orientation of ups and downs.
The biggest issue we encountered was to express this pattern
mathematically. This was the most
frustrating because although we know the pattern, we could not express it in a
way that the pattern of creases for any number of folds can be calculated. After doing some research about the problem
at home, I learned that a type of function called recursive function can be
used to predict the pattern. This is
because recursive functions are basically looping functions that uses the
output as the input, thus if we can enter the basic pattern of how the creases
are added, then the final crease pattern can be predicted with the
function.
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