Consider the problem of PARTITION: we are given a set of numbers (if you prefer, you may think of these as positive integers; however, that is not necessarily part of the problem statement). We want to answer the boolean question: is there a subset of these elements whose sum is exactly half of the total? (a) Prove that this problem is in NP. (b) Observe that we could decide this language by making a call to any correct algorithm for Subset Sum with parameter T = (1/2) Xi. Why does this not prove anything about the difficulty of this problem? (c) Prove that this problem is NP-complete.

Which of the following is not contained on the slide show toolbar? a. next button b. slide button c. close button d. pen tool

You need to design a circuit that implements the functions in the following table: s0 s1 function0 0 a + 10 1 a – b1 0 a + b1 1 a – 1s0 and s1 are 1-bit control inputs to select the function of the circuit. inputs a and b are 4-bitnumbers in 2s complement form. the output is also a 4-bit number in 2s complement form. you are allowed to use only one ttl 7483 4-bit adder to implement all the functions. but anynumber of other components (except the adder) can be used. hint: design a combinational logic circuit to modify the input b and the “carry input” of theadder depending on the control inputs s0 and s1.important: lab grade will depend on the working of the circuit & will be checked of by your labinstructor.1. is the output valid for the following input combinations: a. s0 = 0, s1 = 0, a = 7, b = 3? b. s0 = 0, s1 = 1, a = 7, b = 3? c. s0 = 1, s1 = 0, a = -4, b = -5? d. s0 = 1, s1 = 1, a = -8, b = 6? 2. what is the range of inputs (for both a and b) that will produce the valid output for all the functions?

Me ! evelyn is a manager in a retail unit. she wants to prepare a report on the projected profit for the next year. which function can she use? a. pmt b. round c. division d. what-if analysis