1. The problem asks to find the correct symbolic statement for "Ruth Adams retired and she did not start her concrete business." Let: - $a$ = "Ruth Adams retired" - $b$ = "She started her concrete business" The statement says she retired ($a$) and did not start the business ($\neg b$). This corresponds to the conjunction $a \wedge \neg b$. 2. The problem asks for the correct symbolic statement for "The classroom is empty if and only if it is the weekend, or it is 7am." Let: - $p$ = "The classroom is empty" - $q$ = "It is the weekend" - $r$ = "It is 7am" "If and only if" means equivalence, so $p \leftrightarrow (q \vee r)$. Among the options, $p \leftarrow q \vee r$ means $p$ if $q$ or $r$, which is part of the equivalence but not full. The closest correct symbolic statement is $p \leftarrow q \vee r$. Final answers: - For the first problem: $a \wedge \neg b$ - For the second problem: $p \leftarrow q \vee r$