For each of the following English sentences: if the operators or connectives are truth functional (or if the operator or connectives can be treated truth functionally despite extra meanings), translate the sentences into our notation. Make sure you identify which variables stand for which simple propositions. Jane passed the GRE and was admitted to graduate school, and either the school is lucky or Jane is. P= Jane passed the GRE. Q= Jane was admitted to graduate school. R= The school is lucky. S= Jane is lucky. P and Q and either R or S (P & Q) & (R v S)