Week 5

This week we had our first test which I feel I did really well on as I had practiced a lot before hand doing the previous years test. I think the assignment really helped on this test as a lot of the questions were similar.. This week went into more detail with proofs and proof structures.  We were taught how to prove a statement using the contrapositive of the statement.  If we know the statement is true and we know how to prove the statement the we  can simply add a line to the proof to state that the contrapositive is also true since it is equivalent to the statement. We were advised to use contrapositive to prove a statement if proving the reverse direction is easier than proving the original direction. We then went through the steps of proving by contradiction. For a statement which is true if we assume it is false then we should reach a contradiction which results in the statement is true. We were shown the proof by Euclid showing that there are infinitely many prime numbers. This proof seemed difficult at first but now its seems easier to understand after a while of looking at it. We were then shown a proof for an existential statement which was very easy to understand as all we have to do is find one example making our argument true to prove it of false to disprove it.