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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.
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 doesnâ€™t belong to A.
A' = {x: x â‚¬ U and x not â‚¬ A}
Union of sets: C = A U B = {x: x â‚¬ A or x â‚¬ 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.
Intersection of sets: C = A Π B = {x: x â‚¬ A and x â‚¬ 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}
Difference of sets: A â€“ B = {x: x â‚¬ A and x â‚¬ B}
e.g.: A = {a,e,i,o,u} and B = {a,i,o,k}. Then A â€“ B = {e,u} and B â€“ A = {k}. Hence, A â€“ B not equal to B - A
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}
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"