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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: ioaus09 on March 22, 2010, 11:32:11 pm

Title: Random questions that I need help with
Post by: ioaus09 on March 22, 2010, 11:32:11 pm: Just wondering if anyone knows the answer of the question: How many elements does P(X) have, if |X| = 3?

also can anyone show me how to find it thanks :)
Title: Re: Random questions that I need help with
Post by: /0 on March 22, 2010, 11:37:20 pm: Not sure if this belongs in spesh =P

Ok, so X has 3 elements. Let's call them:

$X = \lbrace a,b,c\rbrace$ .

$\mathcal{P}(X)$ is the set of all subsets of X.

$\mathcal{P}(X) = \lbrace \lbrace \emptyset\rbrace, \lbrace a \rbrace, \lbrace b \rbrace, \lbrace c \rbrace, \lbrace a,b\rbrace, \lbrace a,c\rbrace, \lbrace b,c\rbrace ,\lbrace a,b,c\rbrace \rbrace$

(the null set is included since it is the subset of X with no elements!)

Have a go at showing that, in general, $|\mathcal{P}(X)| = 2^{|X|}$ (try a counting argument)
Title: Re: Random questions that I need help with
Post by: TrueTears on March 22, 2010, 11:38:44 pm: Quote from: /0 on March 22, 2010, 11:37:20 pm
Have a go at showing that, in general, $|\mathcal{P}(X)| = 2^{|X|}$ (try a counting argument)
or try it algebraically, both ways are awesome :)

[i remember this was one of the first proofs i did when i started combinatorics xD]
Title: Re: Random questions that I need help with
Post by: ioaus09 on March 22, 2010, 11:39:31 pm: ah oops wrong area lol, thanks anyway