Page 1 - SET-Basic-sheet-for-free-course

Set & Function Free Basic Course by-Munna Sir

 (Union of sets) :
†mU A B
A  B
 (Intersection of sets) :
cvV m¤úwK©Z MyiæZ¡c~Y© welqvw` A B A
 B A B A intersection B.
 (Disjoint set)
 (Set)
A, B, C, D,
 (One–One Correspondence) A
X, Y a, b, c, d, x, y
B B
A
 (Universal set) :
A B
U S
 (Equivelent set) : A B
 (Subset) : A = {1, 2, 3, 4}, B = {1, 2, 3} C = {1, 2, 3,
A  B A B
4} B A
A B A ~ B
B A
B  A.

 (Proper Subset) A B
B A
A B
 (Empty set) :  Union A  B
{ }   Intersection A  B
 Proper subset A  B
 Subset A  B
 (Equality of sets)
 not subset A  B
 Belongs to x  A
 (Difference of sets) A \ B A B
 not belongs to x  A
B A A \ B

 null set  = { }
 (Complementary set) : A U
 Prime A = { x  U
A
x  A}
A A
: such that A = { x : x 
c
A A R}
 (Power set) : A A

P(A)
(i) A B n (A  B) = n (A) + n (B)  n(A  B)
 (Venn Diagram)
(ii) A, B C
 n (A  B) = n(A) + n(B) [  A  B = 0]
 n (A  B  C) = n(A) + n(B) + n(C)
(iii) A, B C
A B U A B U U (iv) n(A  B  C) = n(A) + n(B) + n(C)  n(A  B)  n(B  C)
 n(C  A) + n(A  B  C)
A A
(v) n(A) = n(U)  n(A)

A  B A  B

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