91Ó°ÊÓ

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 \(|f(x)-f(a)|<\varepsilon\)

Use truth tables to show that the following statements are logically equivalent. \(\sim(P \vee Q \vee R)=(\sim P) \wedge(\sim Q) \wedge(\sim R)\)

Use truth tables to show that the following statements are logically equivalent. \(\sim(P \wedge Q \wedge R)=(\sim P) \vee(\sim Q) \vee(\sim R)\)

Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. Some sets are finite.

Negate the following sentences. There exists a real number \(a\) for which \(a+x=x\) for every real number \(x\).

Be sure to also state exactly what statements \(P\) and \(Q\) stand for. There is a quiz scheduled for Wednesday or Friday.

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.

Negate the following sentences. I don't eat anything that has a face.

Translate each of the following sentences into symbolic logic. There exists a real number \(a\) for which \(a+x=x\) for every real number \(x\).

Write the following as English sentences. Say whether they are true or false. $$ \forall X \subseteq \mathbb{N}, \exists n \in \mathbb{Z},|X|=n $$