Chapter 2: Problem 9
Negate the following sentences. If \(\sin (x)<0\), then it is not the case that \(0 \leq x \leq \pi\).
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Use truth tables to show that the following statements are logically equivalent. \(\sim(P \vee Q \vee R)=(\sim P) \wedge(\sim Q) \wedge(\sim R)\)
Translate each of the following sentences into symbolic logic. If \(x\) is a rational number and \(x \neq 0,\) then \(\tan (x)\) is not a rational number.
Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. Sets \(\mathbb{Z}\) and \(\mathbb{N}\) are infinite.
Translate each of the following sentences into symbolic logic. For every positive number \(\varepsilon,\) there is a positive number \(\delta\) for which \(|x-a|<\delta\) implies \(|f(x)-f(a)|<\varepsilon\)
Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. If \(x\) and \(y\) are real numbers and \(5 x=5 y\), then \(x=y\).
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