Dillesh4096 wrote:
gmatt1476 wrote:
The cardinality of a finite set is the number of elements in the set. What is the cardinality of set A ?
(1) 2 is the cardinality of exactly 6 subsets of set A.
(2) Set A has a total of 16 subsets, including the empty set and set A itself.
DS06351.01
Let 'n' be the cardinality of set A.
(1) 2 is the cardinality of exactly 6 subsets of set A.
Number of 2 sets that can be formed from a set of n elements = nc2 = 6
--> n(n-1)/2 = 6
--> n(n-1) = 12 = 4*3
By comparison, n = 4
So, Cardinality of set A = 4 --
SufficientFormula: Number of subsets possible for a set of n elements = \(2^n\) (including the empty set & the set itself)
E.g: If Set A = {1, 2, 3}, All subsets possible = {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}, {} = 8 subsets i.e, \(2^3\) (2) Set A has a total of 16 subsets, including the empty set and set A itself.
--> \(2^n\) = 16
--> n = 4
So, Cardinality of set A = 4 --
SufficientIMO Option D
I am honestly completely lost on this one, seems that I have a completely different idea on what the problem is asking.
When I read "cardinality", I understand basically the number of elements in a set. Following this, my interpretation of the question is if I can know the number of elements in set A.
1) 2 is the cardinality of exactly 6 subsets of set A.
There are 6 subsets in set A with 2 elements INSUFFICIENT - THERE COULD BE OTHER SUBSETS IN A OR EVEN SOME OF THE ELEMENTS CAN BELONG TO MULTIPLE SUBSETS
II) Set A has a total of 16 subsets, including the empty set and set A itself INSUFFICIENT - NO INFORMATION ON NUMBER OF ELEMENTS IN SET A
I)-II) INSUFFICIENT - WE KNOW THAT 6 OUT OF THE 16 SUBSETS OF SET A HAVE " ELEMENTS; YET WE DO NOT KNOW HOW MANY ELEMENTS THE OTHER 10 SUBSETS HAVE NOR IF SOME ELEMENTS ARE IN MORE THAN 1 SUBSET
Clearly the question is going in a completely different direction than my line of though, can someone PLEASE help me explain where do I get completely lost?
Thank you!!!