This weeks classes are about quantifiers,
sentences, symbols and implications. All of those things come into my mind in a
week which makes me feel a little bit confused. I think I need
to organize them in this weekend. Quantifiers and sentences do not
mess me up, but implication does.
Symbols are the easiest one for me, thanks
for MAT223!!! In this semester Mat224 also include symbols. But
there is a new one the symbol of negation, if I understand correct this
symbol means non or not.
I want to say something about implication. In English, the definition of implication is "if...then". In other words, implication means giving a qualification and then geting a result. The following sentence is an example: " if today is raining, then you will need to bring an umbrella. But I am not very clear about the contrapositive and converse.The original implication is "if x, then y". In my opinion, the contrapositive for that is " if non-y, then non-x". Also
I think in contrapositive, if the original implication is True, then the
contrapositive of that implication is True.The definition of converse in logic is the same as its English meaning . Also in my opinion, the original implication is 'if x, then y'
and this is True. The converse of that implication is 'if y, then x' but we
cannot figure out whether this is True or False. For example, in calculus, my high
school teacher said if a function is differentiable on it domain, then it
is continuous on its domain, but if a function is continuous on its
domain, we don't know that is differentiable on its domain and the counter
example is y = abs (x). I hope my understanding is right.
Finally, I want to thanks for
the tutorial problem set, because that helps me understanding the Venn
diagram. It's really helpful.