Steps would help me understand this practice problem, thanks!

Design a combinational circuit with three inputs, x,y, and z, and three outputs, A, B, and C. When the binary input is 0,1,2, or 3 , the binary output is one greater than the input. When the binary input is 4,5,6, or 7 , the binary output is two less than the input. a. Derive the truth table b. Derive the simplified Boolean expressions from the truth table. Notice 1: Apply the minterms only (DO NOT USE K-map)! Notice 2: For the case of B, its expression should include an XOR gate! c. Draw the logic diagram for only C using its simplified Boolean expression