Consider the recurrenceT(n).T(n)={cifn=04T(⌊n4⌋) +12nifn>0a) State and prove by induction a theorem showingT(n)∈O(nlog2n).
b) State and prove by induction a theorem showingT(n)∈Ω(nlog2n).GradingYou will be docked points for functions in the wrong order and for disorganization, unclarity, or incomplete proofs.

Arrange the steps to solve this system of linear equations in the correct sequence. x + y = -2 2x – 3y = -9 tiles subtract 3x + 3y = -6 (obtained in step 1) from 2x – 3y = -9 (given) to solve for x. substitute the value of x in the first equation (x + y = -2) to get y = 1. the solution for the system of equations is (-3, 1). x = -15 the solution for the system of equations is (-15, 13). add 3x + 3y = -6 (obtained in step 1) to 2x – 3y = -9 (given), and solve for x. x = -3 substitute the value of x in the first equation (x + y = -2) to get y = 13. multiply the first equation by 3: 3(x + y) = 3(-2) 3x + 3y = -6.