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Mice21 [21]
3 years ago
15

Can someone help me ASAP with these two postulate questions? I will mark Brainliest if right!!! Explain!!!

Mathematics
1 answer:
Over [174]3 years ago
8 0

Answer:

HL

I'm pretty sure if sorry

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A sel contains eleven elements.
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  • a) 2048
  • b) 2047

=============================================================

Explanation:

If a set has n elements inside it, then it has 2^n different subsets.

Consider a set like {a,b,c}. It has n = 3 elements.

It has 2^n = 2^3 = 8 subsets

Those 8 subsets are...

  1. {a,b,c} ..... any set is a subset of itself
  2. {a,b}
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In that list, items 2 through 4 represent subsets with exactly two things inside it. Items 5 through 7 are known as singletons as they only have one item inside each set. The empty set can be written with the symbol \varnothing or you could have a pair of braces with nothing inside them. The empty set is a subset of any set.

--------------

Note how I included {a,b,c} as a subset. Any set is a subset of itself.

A proper subset will ignore the original set and only look at smaller subsets. If we say B is a proper subset of A, then set B will have fewer items compared to set A. Without the "proper" in there, it's possible that A = B.

So all we've done really is kick out one set which drops 2^n to (2^n)-1 when counting the number of proper subsets. I'm using parenthesis to indicate the "-1" is not part of the exponent. If you wrote this on your paper, then you would likely write 2^{n} - 1

--------------

For this problem, n = 11

This means there are 2^n = 2^11 = 2048 subsets and (2^n)-1 = 2048-1 = 2047 proper subsets.

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