Exercise 1 Conjectures 5 credits each Here are a collection of conjectures. Which are true, and which are false? . If it is true, provide a formal proof demonstrating so. . If it is false, give a counterexample, clearly stating why your counterexamples satisfies the premise but not the conclusion. (No marks for just starting True/False.) Hint: There's quite a few questions here, but each is relatively simple (the counterexamples aren't very complicated, and the proofs are short.) Try playing around with a few examples first to get an intuitive feeling if the statement is true before trying to prove it. Let V be a vector space, and let (, .) : V x V - R be an inner product over V. 1. Triangle inequality for inner products: For all a, b, ce V, (a, c)