Week 5
This week I learned more about proofs; different proof outlines and some techniques I could use when trying to prove cases. One of the proof structures learned was "proof by contradiction":
Assume ¬ Q # in order to derive a contradiction
.
. # some steps leading to contradiction
.
Then ¬ P # contradiction, since P is know to be true
Then Q #since assuming ¬ Q leads to contradiction
Tuesday, December 2, 2014
Journal #3
Week 4
PROOFS!! Proofs are always my biggest enemies as I can tell if something is correct or not but not be able to explain the reason. This week I learned how to write proofs and some structures that are used when writing proofs.
For example:
"A generic proof of ∀x ∈ D, p(x) ⇒ q(x)
Assume x ∈ D # x is a generic element of D
Assume p(x) # x has property p, the antecedent
Then ...
.
.
.
Then ...
Then p(x) ⇒ q(x) #assuming antecedent leads to consequent
Then ∀x ∈ D, p(x) ⇒ q(x) # only assumed x is a generic D "
PROOFS!! Proofs are always my biggest enemies as I can tell if something is correct or not but not be able to explain the reason. This week I learned how to write proofs and some structures that are used when writing proofs.
For example:
"A generic proof of ∀x ∈ D, p(x) ⇒ q(x)
Assume x ∈ D # x is a generic element of D
Assume p(x) # x has property p, the antecedent
Then ...
.
.
.
Then ...
Then p(x) ⇒ q(x) #assuming antecedent leads to consequent
Then ∀x ∈ D, p(x) ⇒ q(x) # only assumed x is a generic D "
Journal #2
Week 3
This week I learned about the conjunctions, ∧ (and) and ∨(or). These two symbols are very similar to the union (∪) and intersection (∩) symbols for sets, and similar in meaning too, therefore these two new symbols are easy to remember. Furthermore, this week I learned how the languages we speak everyday can be very ambiguous, while the languages used to communicate between the machines and us humans need to be indeed precise. This week, the concepts of commutative, associative, and distributive properties of the implications were also introduced; they were confusing at first, but after explanations and various methods of ways to think about these concepts, these properties became clearer to me.
This week I learned about the conjunctions, ∧ (and) and ∨(or). These two symbols are very similar to the union (∪) and intersection (∩) symbols for sets, and similar in meaning too, therefore these two new symbols are easy to remember. Furthermore, this week I learned how the languages we speak everyday can be very ambiguous, while the languages used to communicate between the machines and us humans need to be indeed precise. This week, the concepts of commutative, associative, and distributive properties of the implications were also introduced; they were confusing at first, but after explanations and various methods of ways to think about these concepts, these properties became clearer to me.
Journal #1
Week 2
This week started with the introduction of universal and existential quantification, then implications, converses, and contrapositives. Although I was introduced with the idea of quantifiers and implications briefly last year, it still took me a little bit of time to be able to understand an implication. But overall, this week's material was easy to understand.
This week started with the introduction of universal and existential quantification, then implications, converses, and contrapositives. Although I was introduced with the idea of quantifiers and implications briefly last year, it still took me a little bit of time to be able to understand an implication. But overall, this week's material was easy to understand.
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