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cs2022a16quiz03.pdf - Ma2201/CS2022 Quiz 0011 Discrete...

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Ma2201/CS2022 Discrete Mathematics A Term, 2016 Quiz 0011 Print Name: Sign: 1. ( 4 pts ) Let p be the statement “I have slept five hours”. Let q be the statement “I have a hot cup of coffee”. Let r be the statement “I get up in the morning”. Which of the following expresses the statement I cannot get up in the morning unless I have slept five hours and have a hot cup of coffee. Choose all that are correct. ( p q ) ( ¬ r ⇒ ¬ p ) p ( q r ) ( q r ) p ¬ p ( q r ) When is it false? If he gets up in the morning and has either not slept five hours, or has no cup of coffee. So the statement is ¬ ( r ( ¬ p ∨ ¬ q ). By Demorgan’s law it is ¬ r ( p q ). So the given statement is always true if r is false, and only the third statement has that property. But the third statement is always true if p is true, which is not a property of the given statement. So none of the statements are equivalent to the given statement.
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