- #1

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## Homework Statement

{∅,{∅}}

## Homework Equations

## The Attempt at a Solution

My answer is {∅, {{∅}}, {∅, {∅}}}

but the actual answer is: {∅,{∅},{{∅}},{∅,{∅}}}

I don't understand how the second element, {∅}, appears...

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- Thread starter Bashyboy
- Start date

- #1

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{∅,{∅}}

My answer is {∅, {{∅}}, {∅, {∅}}}

but the actual answer is: {∅,{∅},{{∅}},{∅,{∅}}}

I don't understand how the second element, {∅}, appears...

- #2

jedishrfu

Mentor

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{ nullset, {a}, {b}, {a,b} }

and in your example then the { a } corresponds to the { nullset } and the { b } corresponds to { { nullset } }

- #3

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Okay, thank you.

- #4

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- #5

jedishrfu

Mentor

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000000 represents the nullset { }

100000 represents the first element {a}

010000 the 2nd { b }

001000 the 3rd... { c }

111000 a subset containing {a,b,c}

...

111111 the set itself { a,b,c,d,e,f }

so in creating a subset then

a is or isnt in the subset: 2 choices

b is or isnt in the subset : x 2 =4 choices

...

f is or isn't in the subset x 2 = 64 choices

or more succinctly:

a x b x c x d x e x f

2 x 2 x 2 x 2 x 2 x 2 = 2^6 = 64 possible subsets

and therefore the powerset contains 64 elements.

- #6

HallsofIvy

Science Advisor

Homework Helper

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Suppose that, for some number k, any set with k member has 2

1) If subset B of A does not contain x, it is a subset of A\{x}. Since A contains k+1 members, A\{x} contains k and so has 2

2) If subset B contains x, then B\x does not and so is a subset of A\{x}. That is, eery subset containing x is just a subset that

Therefore, there are 2

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