Chapter 2: Problem 3
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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Negate the following sentences. If \(f\) is a polynomial and its degree is greater than \(2,\) then \(f^{\prime}\) is not constant.
Use truth tables to show that the following statements are logically equivalent. \(P \Rightarrow Q=(\sim P) \vee Q\)
Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " You fail only if you stop writing. (Ray Bradbury)
Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " Whenever a surface has only one side, it is non-orientable.
Write the following as English sentences. Say whether they are true or false. $$ \forall x \in \mathbb{R}, \exists n \in \mathbb{N}, x^{n} \geq 0 $$
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