q2 and q 3

elements in this ordering? 2. Let N be the set of all natural numbers. Let S1 (ASN|A is infinite }, S2 = { A N I A is finite and S = S1 x S2. For (A1,B1) E S and (A2,B2) E S, define a relation R such that (A1,B1) R (A2,B2) iff A1CA2 and B2CB1. i) Is R a total order? Justify. i) Does S have a least/largest element? Justify. 3. Consider the set of all possible polynomials which can be formed which have integer coefficients. Is this set countable or uncountable? *4. We know that a set S is said to be countable if there exists a bijection from S to N, the set of natural numbers. Find a bijection from N x N to N to prove that N x N is countable. **5. The method to prove that the set S containing total number of binary strings is uncountable is called Cantor's diagonalization (Flipping the diagonal elements). Why can't the same logic be applied to prove that the set of rational