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

Mathematics

1 answer:

-BARSIC- [3]3 years ago

3 0

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)$\\Pat watched the news this morning implies that Sam had pizza last night or Chris finished her homework$

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Step-by-step explanation:

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