E.125. Aflați numărul elementelor mulțimilor AAA și BBB, dacă A={x∈N∣6<x≤2020}A=\{x\in \N \mid 6 < x \leq 2020\}A={x∈N∣6<x≤2020} și B={x∈N∣22015<x≤22020}B=\{x\in \N \mid 2^{2015}<x\leq 2^{2020} \}B={x∈N∣22015<x≤22020}.
Răspuns: Card A=2014Card~A=2014Card A=2014, Card B=31⋅22015\quad Card~B=31 \cdot 2^{2015}Card B=31⋅22015
A={7,8,9,⋯ ,2020}⇒card A=(2020−7)+1A=\{7, 8, 9, \cdots, 2020\} \Rightarrow card~A=(2020-7)+1A={7,8,9,⋯,2020}⇒card A=(2020−7)+1. Deci card A=2014\boxed{card~A=2014}card A=2014.
card B=22020−(22015+1)+1=22020−22015=22015(25−1)card~B=2^{2020} - (2^{2015}+1)+1 = 2^{2020}-2^{2015}=2^{2015}(2^5-1)card B=22020−(22015+1)+1=22020−22015=22015(25−1). Deci card B=31⋅22015\boxed{card~B=31 \cdot 2^{2015}}card B=31⋅22015.