Week 3

This week we started off by being introduced to the Conjunction (and) and Disjunction (or) which were made easy to understand by providing their set notation counterparts. I understood conjunction to occur when an element has two properties therefore two predicates hold true for that element. I also learned that we need to be careful with the and in English sentences as there could be confusion between there existing an element of each predicate and there existing an element which holds true for both predicates. I understood dis-junction to occur when at least one of  two the two predicates have to be true. Again I learnt that we need to be careful with the or in English sentences as they could be exclusive meaning that only one of two predicates may hold true for an element where as in dis-junction both predicates could hold true for an element but at least one must hold true.

The next topic we went on to discuss was negation which I understood to be the complete opposite of a logical expression.I found it very simple to negate a whole expression but it got a little tricky to place the negation sign on the smallest component of an expression. This became easier when we were introduced to the idea of negating an expression part by part. To negate a universal quantifier we use an existential quantifier. To negate an existential quantifier we use a universal quantifier. Then we just logically negate the predicates and/or implications in the expression.

We also covered the importance of placing required brackets in the right places to indicate the scope conjunctions, dis-junctions, and implications as without brackets there could be multiple meanings of an expression.

The last topic we covered this week was truth tables which should be used to represent expressions in the case that there are too many predicates which would create a very confusing Venn Diagram. i found these tables very interesting as we can easily access data from them to determine whether an expression is true or false and these tables can also be easily implemented into a program. The topic I found challenging was DeMorgans law an I plan to pay more attention to understand the exact meaning.

Week 1-2

Just from the introduction of CSC165 this course seems very interesting. I am really exited to learn how solve problems using mathematical expression and reasoning and apply these methods in programming. I also enjoyed seeing how a paragraph written in English could be translated into math making it easier to withe a program to complete whatever tasks or requirements that were in the program. In particular I enjoyed the example of how a user may ask a machine to find a phone with certain requirements which we can express mathematically and create a program to complete the tasks.

The next topic we discussed in class was precision and how precise or ambiguous to be in certain tasks. I found it very interesting how to successfully communicate with anyone we have to be the right amount of precise or ambiguous. For instance when we communicate to other humans we should be as precise as needed but when we communicate to a computer or when a computer communicates with us a high level of precision is needed.

Then we continued onto analyzing statements classifying elements of sets. Initially I found this a bit challenging as I could no picture the elements and the sets that a particular statement would refer to. But then when we were shown how ti show these elements in sets in the form of a Venn diagram, I found it a lot easier to picture the situations. The Venn diagrams helped me again when we started falsifying or verifying quantified claims as I could now easily picture what cases would have to occur for a statement to be true of false. Then i was also able identify what programs could analyze the quantified claims and also what input parameters to pass into the program to analyze the claims.

The last topics we went onto were sentences,  statements, implications, and predicates. I understood that sentences are phrases we cannot verify or falsify without further knowledge but statements can be verified or falsified.  In the predicates section we learns that if an element x has a property L then we can write L(x) to express this. When we continued onto implications, I was getting confused on the tricky phrases in identifying the assumption and the consequence. I plan on paying closer attention in class this coming week to get a better understanding of implications. Although I was able to understand the concept of Vacuous truth as even though logically an assumption or consequence is incorrect  if it is not possible to show that they are incorrect, the statement is taken to be true. That is where we ended off for the week.