Question

what are the laws of sets in math?

Answer 1

Well, it is related to SET THEORY..

Answer 2

@camzieeee
these are laws of set:
i)Commutative laws
ii)Associative laws
iii)Distributive laws
iv)Identity laws
v)Complement laws
vi)Impotent laws
vi)Domination laws
vii)Absorption laws

Answer 3

Can I jump right in? lol
The main things we do are taking union, taking intersection, and taking the complement.
First, we let
U
denote the universal set, that is to say, all elements are in U
In taking the union\[A \cup B\]We mean all elements that are in A or B (or both)
In taking the intersection\[A \cap B\]We mean all elements that are in A and B have in common

In taking the complement
\[A' or A^{c}\]You could say this means all elements in U but NOT in A.

Ok, Commutative law:
\[A \cup B = B \cup A\]\[A \cap B = B \cap A\]
Now Associative law:
\[(A \cup B) \cup C = A \cup (B \cup C)\]\[(A \cap B) \cap C = A \cap (B \cap C)\]
Then Distributive law:
\[A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\]\[A \cup (B \cap C) = (A \cup B) \cap (A \cup C)\]

For the Identity laws, take into consideration that
\[\emptyset = the \ Empty \ or \ Null \ Set\]
Or simply the set with no elements.
first:
\[A \cup \emptyset = A\]Makes sense, right? If you take elements from Set A and an empty set, you'll still get the elements of A.
\[A \cap U = A \]Think about it, what do the universal set and A have in common, if you know that ALL elements are in U? :)

Answer 4

Complement laws:
\[A \cup A' = U\]\[A \cap A' = \emptyset\]So, basically, if you take elements in both A and all things NOT in A (A'), then you'll get every conceivable element (U)
And if you take what A and A' (which is all things NOT in A), you'll get nothing, by definition, they have nothing in common :D

Answer 5

Idempotent laws:
\[A \cup A = A\]\[A \cap A = A\]
So... if you take elements from (ehem) both A and A, you'll get elements from A
And what do A and A have in common? A, of course ;)

Answer 6

i have a document

Answer 7

Domination laws:
\[A \cup U = U\]\[A \cap \emptyset = \emptyset\]
So, if you take elements from both A and U, all of them will still be in U and
If you take what elements A and an empty set have in common, there'll be none, as there were no elements in the null set anyway :)