The minimum number of $$JK$$ flip-flops required to construct a synchronous counter with the count sequence $$\left( {0,0,1,1,2,2,3,3,0,0,...} \right)$$ is ____________.

Let $$X$$ and $$Y$$ denote the sets containing $$2$$ and $$20$$ distinct objects respectively and $$𝐹$$ denote the set of all possible functions defined from $$X$$ to $$Y$$. Let $$f$$ be randomly chosen from $$F.$$ The probability of $$f$$ being one-to-one is ________.

The number of onto functions (subjective functions) from set $$X = \left\{ {1,2,3,4} \right\}$$ to set $$Y = \left\{ {a,b,c} \right\}$$ is __________________.

Which one of the following well formed formulae is a tautology?