What is a Boolean Function?

Question

Please explain to me what a Boolean function is, and how do I make an expression.

If the statement states that $f=$"she is out of work" and $s=$"she is spending more", how can I write symbolically that ($a$) "Neither is she out of work nor is she spending more"?

Answer 1

Not generally speaking, a Boolean function is a function $f:Domain \rightarrow \{true,false\}$.
If you define $f$ as "She is out of work" and $s$ as "She is spending more" then (a) would be: $$\lnot f \land \lnot s$$

Answer 2

For a state $x$ describing her, the two Boolean functions can be defined as follows:

$ f(x) = \begin{cases} 1 & \textrm{ if x = she is out of work} \\ 0 & \textrm{ if x = she is not out of work} \\ \end{cases}$

$ s(x) = \begin{cases} 1 & \textrm{ if x = she is spending more} \\ 0 & \textrm{ if x = she is not spending more} \\ \end{cases}$

Thus, in symbolic form, (a) can be written as $f = 0 \land s=0$.