Are the following statements true or false?
1. Let P(n) be the statement "If any string of length n over {a,b} has more a's than b's, then it has two a's in a row". We canprove this statement is true for all n with n ? 2 by proving P(2),P(3), and "for all n: P(n) ? P(n+2)".
2. Let P(x) be a predicate with one free variable x of typenatural. If I prove P(0), "for all x: P(x) ?P(x+2)", and "for all x: P(x) ? P(x+3)", I may conclude "for all x:P(x)".
