Chegg is providing the wrong solution I need a correct answe

Chegg is providing the wrong solution. I need a correct answer and solution.

Consider the system shown in Figure P4.35-1. For parts (a) and (b) only, X_c(j Ohm) = 0 for |Ohm| > 2 pi times 10^3 and H(e^j omega) is as shown in Figure P4.35-2 (and of course periodically repeats). Determine the most general condition on T, if any, so that the overall continuous-time system from x_c(t) to y_c(t)is LTI. Sketch and clearly label the overall equivalent continuous-time frequency response H_eff(j Ohm) that results when the condition determined in (a) holds. For this part only assume that X_c (j omega) in Figure P4.35-1 is bandlimited to avoid aliasing, i.e., X_c(j Ohm) = 0 for |Ohm| greaterthanorequalto pi/T. For a general sampling period T, we would like to choose the system H(e^j omega) in Figure P4.35-1 so that the overall continuous-time system from xc(t) to y_c(t) is LTI for any input x_c(t) bandlimited as above. Determine the most general conditions on if any, so that the overall CT system is LTI. Assuming that these conditions hold, also specify in terms of H(e^j omega) the overall equivalent continuous-time frequency response H_eff (j Ohm)

Solution

Yes, this system is LTI. However, this system is LTI, we have to find a general condition for T.