Chapter 2: Problem 8
Use truth tables to show that the following statements are logically equivalent. \(\sim P \Leftrightarrow Q=(P \Rightarrow \sim Q) \wedge(\sim Q \Rightarrow P)\)
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Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " An integer is divisible by 8 only if it is divisible by 4
Negate the following sentences. If \(x\) is a rational number and \(x \neq 0,\) then \(\tan (x)\) is not a rational number.
Negate the following sentences. For every positive number \(\varepsilon\), there is a positive number \(M\) for which \(|f(x)-b|<\varepsilon\) whenever \(x>M\).
Translate each of the following sentences into symbolic logic. You can fool some of the people all of the time, and you can fool all of the people some of the time, but you can't fool all of the people all of the time. (Abraham Lincoln)
Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. \(\cos (x)=-1\)
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