PLEASE SOLVE THIS QUESTION WITH PROPER REASONING

3. A digital logic unit consists of 3 input signals A,B, and C, respectively, and an output signal F. The output produces a HIGH (1) either when inputs B&C are equal or when A is LOW (0). However, it is impossible for all 3 inputs to be the same value (Hint: Don't care cases). (1 extra credit point) a. Obtain the truth table b. Draw the K-map and find both the minimal SOP and POS c. Draw the logic circuit based on the SOP equation obtained in (b) d. Demonstrate a working prototype using the POS expression obtained in (b). Explain how you know the circuit works. (Video submission is on Canvas)