Week 5 Term Test ~ Contradiction, existence, sequences

Proof using contrapositive

the proof for P IMPLIES Q also proves NOT Q IMPLIES NOT P, and vice versa

Hence we can prove P IMPLIES Q by proving its contrapositive 

Use when the reverse direction is easier to prove than the original

Proof using contradiction

Assume predicate logic P, then by P and some axioms we come to a contradiction, hence NOT P

Proof for existence

Find a single example, show the predicate logic applies

Proof about a sequence

It is not much different as proving a regular expression, the key is to take the sequence definition as predicates, often works better if you write out the first 10 terms of the sequence to visualize it.