True or False. T = true, F = false, and O = open, meaning that the answer is not known science at this

time. In the questions below, P and NP denote P-time and NP-time, respectively.

(i)The set of strings that your high school algebra teacher would accept as legitimate expressions is a context-free language (ii)The language (e consisting of just one string, the empty string, is N'P-complete. Warning Think long and hard about this problem before you answer. It's not as easy as it seems (ii)T The empty language is NP-complete. Warning. Think long and hard about this problem before you answer. It's not as easy as it seems. (iv)There exists a polynomial time algorithm which finds the factors of any positive integer, where the input is given as a binary numeral. (v)The language consisting of all strings over (a, b) which have more a's than b's is context-free. (vi) 2-SAT is p.TI ME. (vii)3-SAT is P-TIME (viii) Primality is P-TIME (ix)There is a P-TIME reduction of the halting problem to 3-SAT