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Equal sets: Two sets A and B are equal if they have exactly

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Equal sets: Two sets A and B are equal if they have exactly [#permalink] New post 17 Jan 2006, 15:03
Equal sets:
Two sets A and B are equal if they have exactly the same elements. A=B
Let A = {1,2,3,4} and B = {3,1,2,4}. Then A=B
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 [#permalink] New post 17 Jan 2006, 15:06
Subsets:
If every element of set A is also an element of set B, then A is called a subset of B. Its denoted as: A C B

Empty set (Φ) is a subset of every set.
Let A = {1,3,5} and B={x:x is an odd number less than 6}, then A C B. Also B C A. Hence, A = B
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 [#permalink] New post 17 Jan 2006, 15:07
Power Set P(A):
is a collection of all subsets of set A.
If A is a set with n(A) = m,
then n[P(A)] = 2^m.

n[P(A)] = number of element in P(A)
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 [#permalink] New post 17 Jan 2006, 15:08
Universal set (U):
is a set U, which contains all the sets under consideration as a subsets of U.
e.g.: For the set B of all integers, the universal set can be a set of all real numbers. It can also be a set of all rational numbers.
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 [#permalink] New post 17 Jan 2006, 15:09
Complement of set:
Let U be the universal set and A is a subset of U. Then the complement of A (written as A')is a set of all elements of U which doesn’t belong to A.
A' = {x: x € U and x not € A}
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 [#permalink] New post 17 Jan 2006, 15:10
Union of sets: C = A U B = {x: x € A or x € B}.
e.g.: For the set B of all integers, the universal set can be a set of all real numbers. It can also be a set of all rational numbers.
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 [#permalink] New post 17 Jan 2006, 15:11
Intersection of sets:
C = A Π B = {x: x € A and x € B}.
Disjoint sets: if A Π B = Φ, then A and B are Disjoint sets.
e.g.: A={2,4,6,8} and B={1,2,6}, then A Π B = {2,6}
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 [#permalink] New post 17 Jan 2006, 15:13
Difference of sets:
A – B = {x: x € A and x € B}
e.g.: A = {a,e,i,o,u} and B = {a,i,o,k}. Then A – B = {e,u} and B – A = {k}. Hence, A – B not equal to B - A
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 [#permalink] New post 17 Jan 2006, 15:14
Application of sets

n(A U B) = n(A-B) + n(A Π B) + n(B-A) = n(A-B)+n(AΠB)+n(B-A)+n(AΠB)-n(AΠB)
= n(A) + n(B) – n(A Π B)
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 [#permalink] New post 26 Dec 2007, 23:35
If a set has 6 elements, the number of subsets is 12. correct?
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 [#permalink] New post 27 Dec 2007, 08:13
bmwhype2 wrote:
If a set has 6 elements, the number of subsets is 12. correct?


If a set has n elements, number of subsets = 2^n
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 [#permalink] New post 27 Dec 2007, 09:00
bmwhype2 wrote:
parsifal wrote:
bmwhype2 wrote:
If a set has 6 elements, the number of subsets is 12. correct?


If a set has n elements, number of subsets = 2^n
why?


How did you get 12 subsets for 6 elements?

Note that you ought to consider null set and the set itself as the subsets.
Let me give you an example of a set with 3 elements S = {a,b,c}
Subsets:
null set
S
{a}
{b}
{c}
{a,b}
{b,c}
{a,c}
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 [#permalink] New post 27 Dec 2007, 09:46
parsifal wrote:
bmwhype2 wrote:
parsifal wrote:
bmwhype2 wrote:
If a set has 6 elements, the number of subsets is 12. correct?


If a set has n elements, number of subsets = 2^n
why?


How did you get 12 subsets for 6 elements?
Note that you ought to consider null set and the set itself as the subsets.
Let me give you an example of a set with 3 elements S = {a,b,c}
Subsets:
null set
S
{a}
{b}
{c}
{a,b}
{b,c}
{a,c}

thanks for the explanation. i was reading someone's math notes i got off the internet. i questioned this concept but i was too tired to think it out. i guess he apparently forgot the caret, which is immensely important to the meaning of the "equation"
  [#permalink] 27 Dec 2007, 09:46
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