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m12#23 - Number System

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m12#23 - Number System [#permalink]

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New post 12 Jun 2010, 06:24
How many subsets of \((a,b,c,d)\) including both \(a\) and \(c\) and (order of elements does not matter) are there?

A) 3
B) 4
C) 5
D) 6
E) 7

OA is B and OE is:
Here are the four subsets: \((a,c)(a,c,b)(a,c,d)(a,c,b,d)\)

I want to know whether \((a)\) and \((c)\) are valid subsets or not?
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Re: m12#23 - Number System [#permalink]

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New post 12 Jun 2010, 08:51
ykaiim wrote:
How many subsets of \((a,b,c,d)\) including both \(a\) and \(c\) and (order of elements does not matter) are there?

A) 3
B) 4
C) 5
D) 6
E) 7

OA is B and OE is:
Here are the four subsets: \((a,c)(a,c,b)(a,c,d)(a,c,b,d)\)

I want to know whether \((a)\) and \((c)\) are valid subsets or not?


Generally \((a)\) and \((c)\) are valid subsets of the set \((a,b,c,d)\), but for this question we are looking for subsets that include both \(a\) and \(c\).

Hope it's clear.
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Re: m12#23 - Number System [#permalink]

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New post 12 Jun 2010, 08:56
Thanks for clearing my doubt.
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Re: m12#23 - Number System [#permalink]

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New post 18 Jun 2011, 00:15
Is (a,b,c,d) is a subset of (a,b,c,d) ?
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Re: m12#23 - Number System [#permalink]

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New post 18 Jun 2011, 00:23
Every set has 2^n subsets where n is the number of elements in the set, and every set is a subset of itself.

Note: Null set is a subset of every set!!!

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Re: m12#23 - Number System [#permalink]

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New post 18 Jun 2011, 01:34
thanks sudhir, so that would mean,

for a set {a,b}, number of subsets = 2^2 = 4.

{null},
{a}
{b}
{a,b}



for the question at hand in this thread : we will have 2^3 = 8 subsets, from which we will remove the null subset,

thus we are left with 7.now order does not matter, so out of the 6 sets formed with{(ac),b,d}, we discard 3 ?
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Re: m12#23 - Number System   [#permalink] 18 Jun 2011, 01:34
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