Question

1. Consider the alphabet set Σ = (0,1,2) and the enumeration ordering on Σ*, what are the 20th and 25th elements in this ordering? 2. Let N be the set of all natural numbers. Let S1 = { Ag N 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 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. Finda biecion from N xN to N to prove that N x Nis countable

q1

Answer 1