Exercise 1.4

Question

Let $A$ and $B$ be sets of real numbers.
Write the negation of each of the following statements:
\begin{enumerate}[label=(\alph*)]
\item For every $a \in A$, it is true that $a^2 \in B$.
\item For at least one $a \in A$, it is true that $a^2 \in B$.
\item For every $a \in A$, it is true that $a^2 
otin B$.
\item For at least one $a 
otin A$, it is true that $a^2 \in B$.
\end{enumerate}

Dan Whitman · Accepted Answer

These are all basic logical negations using existential quantifiers:

(a) There is an $a \in A$ where $a^2 
otin B$.

(b) For every $a \in A$, $a^2 
otin B$.

(c) There is an $a \in A$ where $a^2 \in B$.

(d) For every $a 
otin A$, $a^2 
otin B$.

Exercise 1.4

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Exercise 1.4

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