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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> A finite set <math>\Omega</math> has <math>n</math> elements. Show that if we count the empty set and <math>\Omega</math> as subsets, there are <math>2^n</math> subsets of <math>\Omega</math>.") |
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A finite set <math>\Omega</math> has <math>n</math> elements. Show that if we count the empty set and <math>\Omega</math> as subsets, there are <math>2^n</math> subsets of <math>\Omega</math>. | |||
the empty set and <math>\Omega</math> as subsets, there are <math>2^n</math> subsets of <math>\Omega</math>. | |||
Latest revision as of 23:42, 12 June 2024
A finite set [math]\Omega[/math] has [math]n[/math] elements. Show that if we count the empty set and [math]\Omega[/math] as subsets, there are [math]2^n[/math] subsets of [math]\Omega[/math].