로그부등식 집합

주어진 조건에서 $A ( n ) = \left\{ x \left| 0 < x \leq 2 ^{n} \right\} \right.$, $B ( n ) = \left\{ x \left| 0 < x \leq 4 ^{n} \right\} \right.$이다. ㄱ. $A ( 1 ) = \left\{ x \left| 0 < x \leq 2 \right\} \right.$ (거짓) ㄴ. $A ( 4 )$$= \left\{ x \left| 0 < x \leq 2 ^{4} \right\} \right.$$= \left\{ x \left| 0 < x \leq 4 ^{2} \right\} = B ( 2 ) \right.$ (참) ㄷ. $A ( n ) \subset B ( n )$이면 $2 ^{n} \leq 4 ^{n} = 2 ^{2 n}$ $\therefore n \geq 0$ $\therefore B ( - n ) = \left\{ x \left| 0 < x \leq 4 ^{- n} \right\} \right.$$\subset A ( - n ) = \left\{ x \left| 0 \leq x \leq 2 ^{- n} \right\} \right.$ (참)