Exercise 1.6

Question

Write the contrapositive of each of the statements of \href{./exercise_1-5}{Exercise 5}.

Dan Whitman · Accepted Answer

Again these involve simple logical negations of both sides of the implications:

(a) $x 
otin A$ for every $A \in \mathcal{A} \Rightarrow x 
otin \bigcup_{A \in \mathcal{A}} A$.

(b) $x 
otin A$ for at least one $A \in \mathcal{A} \Rightarrow x 
otin \bigcup_{A \in \mathcal{A}} A$.

(c) $x 
otin A$ for every $A \in \mathcal{A} \Rightarrow x 
otin \bigcap_{A \in \mathcal{A}} A$.

(d) $x 
otin A$ for at least one $A \in \mathcal{A} \Rightarrow x 
otin \bigcap_{A \in \mathcal{A}} A$.

Answers