Final answer:
A 8:1 multiplexer can be used to implement the given Boolean function by assigning the correct control signals to the select lines.
Step-by-step explanation:
A 8:1 multiplexer is used to select one out of eight input signals based on the control inputs. To implement the function Y = BC + A¯B¯C¯ + BC¯ using a 8:1 multiplexer, we need to derive the truth table for this function and determine the control signals for each input combination. The truth table for the function has three inputs (A, B, and C) and one output (Y), and all the possible input combinations can be represented in eight rows. By assigning the correct control signals to the select lines of the multiplexer, the output Y can be obtained.