I want to know how to read mathematical formulas? For example：
Q1: $$ p^\text{new}=\mathop{\arg\max}_{p_j\in P^-}\{r_j\::\:|p_j-p_i|-r_i-r_j\geq 0, \forall p_i\in P^+\}$$ A1: the value p-new is defined of the output of the function arguments of the maxima applied to the set of value in parentheses (How to read the set of value in parentheses out professionally? ).
Q2: $$\mathbf{PD}(P^+\bigcup Q)$$ A2:
Q3: $$P^+\setminus\{p_1,p_2,p_3\}.$$ A3:
Q4: $$|p^\text{new}-p_i|-r^\text{new}-r_i\geq 0,i=1,2,3,$$ A4:
Q5: $$ W_{ij}=\frac{\vert p_i-p_j \vert +\mu\vert r_i-r_j \vert}{\min(r_i,r_j)}.$$
A5:
Q6: $$p_i^f$$ A6:
Q7: $$\mathcal{G}' \text{(the latex code is \mathcal{G}')}$$ A7:
Q8: $$p_j\in \widehat{P^-}$$ A8:
How to read this?