Let X be a finite set. Show that P(X) has 2^|x| elements. Also, show that |2^x|=2^|x|. {Hint: to give a rigorous proof, induct on the number of elements of X.}
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Originally Posted by r7iris Let X be a finite set. Show that P(X) has 2^|x| elements. Also, show that |2^x|=2^|x|. {Hint: to give a rigorous proof, induct on the number of elements of X.} what does small x represent? and by P(X) you mean the power set of X correct?
Originally Posted by Jhevon what does small x represent? and by P(X) you mean the power set of X correct? |x| is the number of member in set X. P(X) is the power set of X.
A subset is determined by deciding whether each of the elements of is in the subset: there are two possibilities for each element , namely and . So the total number of possibilities for the subset is . So . Use this to be more rigorous.
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