Determine whether the given equality is true (T) or false (F). We use standard notation for intervals (open, closed, or half-open) in the set of real numbers. For instance, $[a,b)=\lbrace x \in {\mathbb R} \ | \ a \le x < b \rbrace$, and $(a,\infty)=\lbrace x \in {\mathbb R} \ | \ x > a \rbrace$. The set of positive integers is denoted by ${\mathbb N}$.

 1. $\bigcap_{n \in {\mathbb N}} (\frac{1}{n},n) = \lbrace 1 \rbrace$
 2. $\bigcup_{n \in {\mathbb N}} [\frac{1}{n},n]= [0,\infty)$
 3. $\bigcap_{1\leq n\leq 7} [\frac{1}{n},n] = \lbrace 1 \rbrace$
 4. $\bigcap_{n \in {\mathbb N}} [\frac{1}{n},n] = \lbrace 1 \rbrace$
 5. $\bigcup_{n \in {\mathbb N}} (\frac{1}{n},n) = (0,\infty)$