A set is a well defined collection of objects. Sets are represented in three forms (i) Descriptive form (ii) Set â€“ builder form (iii) Roster form.

**Set Language**

**Points to Remember**

**â€¢ **A set is a well defined collection of
objects.

**â€¢ **Sets are
represented in three forms (i) Descriptive form (ii) Set â€“ builder form (iii) Roster
form.

**â€¢ **If every element of *A* is also
an element of *B*, then *A* is called a subset of *B*.

**â€¢ **If *A*âŠ†*B* and *A*â‰ *B*, then *A* is a proper subset of *B*.

**â€¢ **The power set of the set *A* is
the set of all the subsets of *A* and it is denoted by *P*(*A*).

**â€¢ **The number of subsets of a set with ** m**
elements is

**â€¢ **The number of proper subsets of a set
with ** m** elements is

**â€¢ **If Aâˆ©B = âˆ… then *A* and *B* are disjoint
sets. If Aâˆ©B â‰ âˆ…
then *A* and *B* are overlapping.

**â€¢ **The difference of two sets *A* and
*B* is the set of all elements in *A* but not in *B*.

**â€¢ **The symmetric difference of two sets
*A* and *B* is the union of *A*-*B* and *B*-*A*.

For any two
sets *A* and *B*,

*A*âˆª*B*=*B*âˆª*A *;* A*âˆ©*B*=*B*âˆ©*A*

For any three
sets *A*, *B* and *C*

*A*âˆª(*B *âˆª*C*)=(*A*âˆª*B*)âˆª*C* ; *A*âˆ©(*B *âˆ©*C*)=(*A*âˆ©*B*)âˆ©*C*

For
any three sets *A*, *B* and *C*

*Aâˆ©(B
**âˆª**C)=(Aâˆ©B)**âˆª**(Aâˆ©C) Intersection
over union*

*A**âˆª**(B âˆ©C)=(A**âˆª**B)âˆ©(A**âˆª**C) Union over
intersection*

For any three
sets *A*, *B* and *C*

*A*âˆ’(*B
*âˆª*C*)=(*A*âˆ’*B*)âˆ©(*A*âˆ’*C*)

*A*âˆ’(*B
*âˆ©*C*)=(*A*âˆ’*B*)âˆª(*A*âˆ’*C*)

Consider
an Universal set and *A*, *B* are two subsets, then

(AâˆªB)â€² =Aâ€² âˆ© B â€² ; (Aâˆ©B)â€² =Aâ€²âˆª Bâ€²

If *A*
and *B* are any two sets, then *n* (*A* âˆª *B* ) =
*n*(*A*) + *n*(*B* ) âˆ’*n*(*A* âˆ©
*B*)

If *A*,
*B* and *C* are three sets, then

*n
*(*A *âˆª* B *âˆª*C*)* *=* n *(*A*)* *+*
n *(*B*)* *+*
n *(*C*)* *âˆ’*
n *(*A *âˆ©*
B *)* *âˆ’*
n *(*B *âˆ©*C*)* *âˆ’*
n *(*A *âˆ©*C
*)* *+*
n *(*A *âˆ©*
B *âˆ©*C*)

Tags : Set Language | Maths , 9th Maths : UNIT 1 : Set Language

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9th Maths : UNIT 1 : Set Language : Points to Remember | Set Language | Maths

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