Consider the following theorem: If x is a positive integer that is not divisible by 3, then x2 - 1 is divisible by 3. [3] Rewrite the theorems using quantifiers and predicates. You can use predicates for oddness and divisibility, like a) Divisible(x.y) : x is divisible by y or for any other numerical properties you need to define b) [6] Give a proof for the theorem. Your proof can be informal (in natural language), but it must have a similar structure of a formal proof, with clear steps and correct application of the rules. Recall that to prove a universal statement we start by instantiating the statement with a generic element of the domain and prove it for that item to prove an existential statement we need to find an element of the domain and prove that the statement is true for that element. Hint for this proof if an integer is not divisible by 3, then it can be written as either 3k+1 or as 3k+2 for some integer k