The determination of the matrix given below is $$$\left[ {\matrix{ 0 & 1 & 0 & 2 \cr { - 1} & 1 & 1 & 3 \cr 0 & 0 & 0 & 1 \cr 1 & { - 2} & 0 & 1 \cr } } \right]$$$

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:

Let $$f$$ be a function from a set $$A$$ to a set $$B$$, $$g$$ a function from $$B$$ to $$C$$, and $$h$$ a function from $$A$$ to $$C$$, such that $$h\left( a \right) = g\left( {f\left( a \right)} \right)$$ for all $$a \in A$$. Which of the following statements is always true for all such functions $$f$$ and $$g$$?

Let f: $$\,B \to \,C$$ and g: $$\,A \to \,B$$ be two functions and let h = fog. Given that h is an onto function which one of the following is TRUE?