Which one of the following statements if FALSE?

The control signal functions of a $$4$$-bit binary counter are given below $$($$where $$X$$ “don’t care”$$):$$

The counter is connected as follows:

Assume that the counter and gate delays are negligible. If the counter starts at $$0,$$ then it cycles through the following sequence:

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $$n$$ variables. What is the minimum size of the multiplexer needed?

How many $$3$$ to $$8$$ decodes with an enable input are needed to construct to constant $$6$$ to $$64$$ line decoder without using any other logic gates