Sets Key Part 002

 
 
   2 1.

ก  A  B ก  A !"#ก 6 $  B !"#ก 3 $ %%$"#ก (A  B) ∪ (A ∩ B) (5 ( )  #%*+ (A  B) ∪ (A ∩ B) (A  B) ∪ (A ∩ B) = (A ∩ B′) ∪ (A ∩ B) = A ∩ (B′ ∪ B) = A∩U = A *,-%$"#ก (A  B) ∪ (A ∩ B) %.!(//ก%$"#ก A .0/ก 6


2.

ก  A  B ก U  A ⊆ B %  $/ A ∪ B = B 3 4 " 5$  4 * (5 ( )  %ก607!03%4ก * * 5$7  !-

B A

U */$!0 A ∪ B %7  *8 .097 " $/(6 B B


A

U

3.

ก  A, B  C ก U  A ⊆ B  B ⊆ C %  $/ A ⊆ C 3 4 " 5$  4 * (5 ( )  607!03%4ก !4 5$7  !-

C B A U 4.




ก  A = {x | x %$,!048/*$/ 51  100} B = {y | y %$,$ก!07/กก$/ 100}, C = {z | z %$,$ก!07/กก$/ 100  3  ก#%$(8}/ %%$"#ก B  (A  C) (5 ( )  !4!03%4ก 48/ *8  %ก %"#ก %7 $/ A = {53, 59, 61, 67, 71, 73, 79, 83, 89, 97} - n(A) = 10 B = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} - n(B) = 25 C = {23, 29, 41, 43, 47, 61, 67, 83, 89} - n(C) = 9 A  C = {53, 59, 71, 73, 79, 97} - n(A  C) = 6 B ∩ (A  C) = A  C - n[B ∩ (A  C)] = n(A  C) *,- n[B - (A - C)] = n(B)  n[B ∩ (A  C)] = n(B)  n(A  C) = 25  6 = 19