Set and subset question

[vlad4]

Hi guys,

I hope you can explain the following comparison question that I got on my Official Practice Test 2.

Set S consists of 5 objects.

Quantity A: The number of subsets of set S that consist of 1 object

Quantity B: The number of subsets of set S that consist of 4 objects

The answer is C. To be honest, I do not get the question or the answer.

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It is my understanding that the following things that happen with a set/subsets:
A: {a}, {b}, {c, d, e} --> Here are 2 subsets with 1 object
B: {a, b, c, d}, {e} ---> here is 1 subset with 4 objects

Thus, these numbers don't match but I am sure I am missing something or misunderstanding the question.

[tommywallach]

Hey Vlad,

Set S consists of 5 objects.

Quantity A: The number of subsets of set S that consist of 1 object

Quantity B: The number of subsets of set S that consist of 4 objects

Your thinking about the question was spot on, so I'm not quite sure where you're getting confused.

Quantity A: How many subsets are there with just one object in them? 5. {A}, {B}, {C}, {D}, {E}

Quantity B: How many subsets are there with 4 objects in them? Also 5.

{A}, {B}, {C}, {D}
{A}, {B}, {C}, {E}
{A}, {B}, {D}, {E}
{A}, {C}, {D}, {E}
{B}, {C}, {D}, {E}

Basically, in the first case, each group would just have one of the five elements. in the second case, each group would have one of the five elements left out.

Make sense?

-t