This week we continued to learn about different types of proofs, such as direct (implication - assume A, conclude B), indirect (contrapositive - assume not B, conclude not A), existential (providing an example, universal (proving true for all elements), and falsity (proving the negation). While the format of the proof was quite easy to get, sometimes the tricky part is to come up with the in-between steps. However, we did lots of examples, and I am starting to get the hang of it, and I have more practicing to do since the second assignment is all about the proofs mentioned above.
As well, this week we had another fun activity where we had to come up with all the possibilities of the number of coins that we can rearrange from left to right drawer by exchanging half the coins between them. The result is actually quite surprising, because we can get all arrangements, as shown in the tree below. Note that all the values can be exchanged (for example 3 | 61 means that we can get 61 | 3 as well), simply because my third step was operation r, and not l, which resulted in 48 | 16 instead of 16 | 48.
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