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Create a logic array qualifyingindex with true for any location where the runner is male with a running time less than 8.2. row array runnergenders indicate if a runner if male (m) or female ( f. row array runnertimes indicates the corresponding runner's time.

For each of the following claims, determine whether they are true or false. justify your determination (show your work). if the claim is false, state the correct asymptotic relationship as o, θ, or ω. unless otherwise specified, lg is log2.(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)n+1 =22n =2n =1 =ln2 n =n2 +2n−4 =33n = 2n+1 =√n = 10100 =o(n4) o(2n)θ(2n+7 ) o(1/n)θ(lg2 n) ω(n2 )θ(9n ) θ(2n lg n )o(lg n) θ(1)

Design a pos circuit that displays the letters a through j on a seven-segment indicator. the circuit has four inputs w, x, y, and z which represent the last 4 bits of the uppercase ascii code for the letter to be displayed. thus, if wxyz = 0001 then "a" will be displayed. (any answer with 22 or fewer gates and inverters, not counting any for the inputs, is acceptable)