Question

Let p, q, and r represent the following statements"

Answer 1

Answer:

Step-by-step explanation:

$a. Sam had pizza last night and Chris finished her homework.\\p\wedge q\\\\ b. Chris did not finish her homework and Pat watched the news this morning. \\\neg q \wedge r\\\\ c. Sam did not have pizza last night or Chris did not finish her homework. \\\neg p \vee \neg q$

$d. Either Chris finished her homework or Pat watched the news this morning, but not both. \\q\vee r\\\\ e. If Sam had pizza last night then Chris finished her homework. \\p \rightarrow q\\\\ f. Pat watched the news this morning only if Sam had pizza last night. \\p\leftrightarrow r$

$g. Chris finished her homework if Sam did not have pizza last night. \\\neg p \rightarrow q\\\\ h. It is not the case that if Sam had pizza last night, then Pat watched the news this morning. \\\neg (p\rightarrow r)$

$i. Sam did not have pizza last night and Chris finished her homework implies that Pat watched the news this morning. \\(\neg p \wedge q) \Rightarrow r\\\\ j. q\Rightarrow r \\Chris finished her homework implies that Pat watched the news this morning.$

$k. p \Rightarrow (q \wedge r) \\Sam has pizza last night implies that Chris finished her homework and Pat watched the news this morning.$

$l. \neg p \Rightarrow (q \vee r) \\Sam did not have pizza last night implies that Chris finished her homework or Pat watched the news this morning.$

$m. r \Rightarrow (p \vee q) \\Pat watched the news this morning implies that Sam had pizza last night or Chris finished her homework$