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Algebra Level 2
  • A = A = {letters in the English alphabet}
  • C = C = {Continents}

Find out the value of ∣ P ( A ) ∣ − ∣ P ( C ) ∣ , |P(A)| - |P(C)|, where P ( ) P( ) is the symbol for the power set .


The answer is 67108736.

Shane Sarosh by Shane Sarosh , 15, Singapore

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2 solutions

Hongqi Wang
Jan 16, 2021

2 26 − 2 7 = 67108736 2^{26} - 2^7 = 67108736

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Shane Sarosh
Jan 16, 2021

I'll elaborate on the solution later.

∑ x = 0 26 ( 26 ! x ! ( 26 − x ) ! ) − ∑ x = 0 7 ( 7 ! x ! ( 7 − x ) ! ) = 67108736 \sum_{x=0}^{26} \left( \dfrac{26!}{x!(26-x)!} \right ) - \sum_{x=0}^{7} \left( \dfrac{7!}{x!(7-x)!} \right ) = 67 108 736

1 Helpful 0 Interesting 0 Brilliant 1 Confused

You have to start the summation from zero to get all possibilities, but they cancel each other out so you will still get the right answer(power set includes the null set)

Jason Gomez - 4 months ago

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I realized later, but again, this isn't a full explanation, so I left that bit out. :P

Shane Sarosh - 4 months ago

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