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Question Stats:
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How many subsets of \(\{a,b,c,d\}\) including both \(a\) and \(c\) (order of elements does not matter) are there? A. 3 B. 4 C. 5 D. 6 E. 7
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16 Sep 2014, 00:47
Official Solution:How many subsets of \(\{a,b,c,d\}\) including both \(a\) and \(c\) (order of elements does not matter) are there? A. 3 B. 4 C. 5 D. 6 E. 7 Here are the four subsets: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\). Answer: B
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15 Jan 2015, 11:22
I think this question is good and helpful. Is there a way to solve with combinatorics?



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Re: M1223
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24 Jul 2015, 09:27
Bunuel wrote: Official Solution:
How many subsets of \(\{a,b,c,d\}\) including both \(a\) and \(c\) (order of elements does not matter) are there?
A. 3 B. 4 C. 5 D. 6 E. 7
Here are the four subsets: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B hi, Bunuel, can we count {a,b,c,d} as subset of {a,b,c,d}..?



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Re: M1223
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24 Jul 2015, 09:31
riyazgilani wrote: Bunuel wrote: Official Solution:
How many subsets of \(\{a,b,c,d\}\) including both \(a\) and \(c\) (order of elements does not matter) are there?
A. 3 B. 4 C. 5 D. 6 E. 7
Here are the four subsets: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B hi, Bunuel, can we count {a,b,c,d} as subset of {a,b,c,d}..? ____________________________ Yes.
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Re: M1223
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29 Oct 2015, 08:54
Bunuel wrote: riyazgilani wrote: Bunuel wrote: Official Solution:
How many subsets of \(\{a,b,c,d\}\) including both \(a\) and \(c\) (order of elements does not matter) are there?
A. 3 B. 4 C. 5 D. 6 E. 7
Here are the four subsets: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B hi, Bunuel, can we count {a,b,c,d} as subset of {a,b,c,d}..? ____________________________ Yes. That does not make sense. How can a "sub" set be the same as the set?? {a,b,c,d} is not a subset of {a,b,c,d}. Agree to disagree.



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Re: M1223
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29 Oct 2015, 11:42
danjbon wrote: Bunuel wrote: riyazgilani wrote: hi, Bunuel,
can we count {a,b,c,d} as subset of {a,b,c,d}..?
____________________________ Yes. That does not make sense. How can a "sub" set be the same as the set?? {a,b,c,d} is not a subset of {a,b,c,d}. Agree to disagree. Mathematically B is a subset of A if every member of B is a member of A. So, a set is a subset of itself.
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Re: M1223
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19 Jan 2016, 09:21
Buenel,
I have a (naive) question. Why (D,A,C,B) is not a subset of (A,B,C,D)  when order of elements doesn't matter ?



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Re: M1223
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19 Jan 2016, 09:25
cricketer wrote: Buenel,
I have a (naive) question. Why (D,A,C,B) is not a subset of (A,B,C,D)  when order of elements doesn't matter ? A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)
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Re: M1223
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19 Jan 2016, 09:31
Bunuel wrote: cricketer wrote: Buenel,
I have a (naive) question. Why (D,A,C,B) is not a subset of (A,B,C,D)  when order of elements doesn't matter ? A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.) Thanks a lot. Very helpful/useful concept.



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10 Oct 2016, 22:28
I think this is a poorquality question. Useless question



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Re: M1223
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15 Jul 2017, 12:40
Can this question be reworded to say " include both a & c"?
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Re: M1223
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23 Jul 2017, 09:36
Why we don't consider singletons? (Set of one number here).



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23 Jul 2017, 20:49
Evgart wrote: Why we don't consider singletons? (Set of one number here). Doesn't the question say that the subsets must include at least both a and c?
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Re: M1223
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14 Aug 2017, 08:19
why not {a,d} and {b,d}?



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14 Aug 2017, 08:24
frndabu1 wrote: why not {a,d} and {b,d}? Because the subsets must include both a and c. Neither {a, d} nor {b, d} include both a and c.
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Re: M1223
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14 Aug 2017, 08:45
Great! careful reading!!!



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Re: M1223
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07 Nov 2017, 12:11
the number of subsets from k elements is 2^k here if we consider a and c together as one element (since they are always present together), won't the number of subsets: 2^3 = 8? now a&c will always need to be present, therefore the only remaining subsets: 2^2 = 4
is above understanding correct?



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Re: M1223
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26 Oct 2018, 13:18
Bunuel wrote: Official Solution:
How many subsets of \(\{a,b,c,d\}\) including both \(a\) and \(c\) (order of elements does not matter) are there?
A. 3 B. 4 C. 5 D. 6 E. 7
Here are the four subsets: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B Dear Bunuel, Is there any other way to approach alike questions. What if the subsets were asked for {a, b, c, d, e, f, g}?



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Re: M1223
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04 Nov 2018, 10:34
Is this fair game on the real test? I haven't seen subsets covered anywhere. Any reference material would be helpful....







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