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Chapter: 9th Maths : UNIT 1 : Set Language

Points to Remember

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

Set Language

Points to Remember

A set is a well defined collection of objects.

Sets are represented in three forms (i) Descriptive form (ii) Set – builder form (iii) Roster form.

If every element of A is also an element of B, then A is called a subset of B.

If AB and AB, then A is a proper subset of B.

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

The number of subsets of a set with m elements is 2m.

The number of proper subsets of a set with m elements is 2m -1.

If AB = then A and B are disjoint sets. If AB ≠ then A and B are overlapping.

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

The symmetric difference of two sets A and B is the union of A-B and B-A.

Commutative Property

For any two sets A and B,

AB=BA ; AB=BA

Associative Property

For any three sets A, B and C

A(B C)=(AB)C ; A(B C)=(AB)C

Distributive Property

For any three sets A, B and C

A∩(B C)=(A∩B)(A∩C)   Intersection over union

A(B ∩C)=(AB)∩(AC)   Union over intersection

De Morgan’s Laws for Set Difference

For any three sets A, B and C

A(B C)=(AB)(AC)

A(B C)=(AB)(AC)

De Morgan’s Laws for Complementation

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

(AB)′ =A′ ∩ B ′ ; (A∩B)′ =A′ B′

Cardinality of Sets

If A and B are any two sets, then n (A B ) = n(A) + n(B ) n(A B)

If A, B and C are three sets, then

n (A B C) = n (A) + n (B) + n (C) n (A B ) n (B C) n (A C ) + n (A B C)

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