Ma2201/CS2022Discrete MathematicsA Term, 2016Quiz 0011Print Name:Sign:1. (4 pts) Letpbe the statement “I have slept five hours”. Letqbe the statement “Ihave a hot cup of coffee”. Letrbe the statement “I get up in the morning”.Which of the following expresses the statementI cannot get up in the morning unless I have slept five hours and have a hotcup 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 ifris false, and only the third statement has thatproperty.But the third statement is always true ifpis true, which is not a property of the givenstatement.So none of the statements are equivalent to the given statement.
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