For a database relation $$R(a,b,c,d),$$ where the domains of $$a, b, c, d$$ include only atomic values, only the following functional dependencies and those that can be inferred from them hold:
$$a \to c\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,b \to d$$
This relation is

Given $$\sqrt {\left( {224} \right),} = {\left( {13} \right)_r},$$
The value of the radix' $$r$$ is:

Let $$^ * $$ be defined as $${x^ * }y = \overline x + y,$$ Let $$z = {x^ * }y.$$ Value of $${z^ * }x$$ is

Let $$f\left( {x,y,z} \right) = \overline x + \overline y x + xz$$ be a switching function. Which one of the following is valid?