Week 7

    So this week we did more proofs. I feel somewhat confident, more confident than last week because of the tutorial. Plus, I learned some of the inference rules in the course notes and reviewed them during the lecture slides. So far, I know that there are introduction and elimination rules. Introduction rules allow us to introduce new logic structures (essentially, building the formula). Some introduction rules are:

a) Implication intro.: If A is assumed then B follows, then A => B

b) Universal intro.: If a is assumed to be a generic element of D and P(a) is derived, then you can conclude "For all a that is an element of D, P(a)"

c) Existential intro.: If x is an element of X is shown and if P(x) is shown, then you can conclude that "There exists an x that is an element of X, P(x)"

d) Conjunction intro.: If you know A and you know B, then you can conclude A and B.

e) Disjunction intro.: If you know A then you can conclude A or B.

    On the other hand, elimination rules allow us to break sentences down (essentially, taking the formula apart). Some elimination rules are:

a) Implication elimination: If you know A => B, then A allows you to conclude B. Also, not B allows you to conclude not A. (Opposite of implication intro.)

b) Universal elimination: If you know "For all a that is an element of D, P(a)", the domain allows you to conclude P(a). (Opposite of universal intro.)

c) Existential instantiation: If you know "There exists an x that is an element of X, P(x)", then you can pick an element with that property. (Opposite of existential intro.)

d) Conjunction elimination: If you know A and B, then you can conclude A (or B) separately. (Opposite of conjunction introduction)

and so on...

    Anyways, I think the quiz went well but mostly because the question was exactly the same as an exercise question. So I think I only did well because I remembered the solution from before. But I forgot what to put as a comment for one of the sentences…

    I'm going to meet my a2 group today to start the assignment so hopefully, I learn a lot from this assignment. Hopefully we do well again, especially since these proofs are much longer and more complicated than the exercises.