g Let X be a problem that is in the class NP . For each of the following write if it is " True," "False," or "We don’t know." Justify your answer. (a) Solutions to X can be verified with a polynomial - time algorithm. (b) There is no polynomial - time algorithm for X . (c) If there exists a polynomial - time algorithm for X , then P = NP . (d) If there exists a polynomial - time algorithm for X , then there m ust exist a polynomial - time algorithm for the Traveling Salesman Problem. (e) If there exists a polynomial - time algorithm for the Traveling Salesman Problem, then there must exist a polynomial - time algorithm for X .

Larry sent an email to andy. andy didn't open larry's email but still understood what the message was. how did andy determine the message without opening the email?

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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?