A system has three inputs and one output. The first two inputs, a and b represent two bits. There are two logic gates in the system, AND and OR$.$ If the third input c is $0,$ the inputs a and b are given as inputs to the AND gate and if c is $1,$ they are given as inputs to the OR gate. The output of the system is taken from the corresponding gate that is active at the given time. Draw a diagram representing the system with logic gates, inputs, and outputs. Show how you can combine the AND and OR gate outputs into one output of the system. Derive a truth table for the system.