Question Number 102357 by Cynosure last updated on 08/Jul/20

for A={1,2,3,4,5,6,7},compute the number of:  (a) Subsets of A.  (b) Nonempty subsets of A.  (c) proper subsets of A.  (d) Non empty proper subset of A.  (e) Subsets of A containing three element.  (f) Subsets of A containing 1,2.  (g) Proper subsets of A containing 1,2.  (h) Subset of A with an even number of element.  (i) Subset of A with an odd number of element.  (j) Subsets of A with an odd number of elements, including the element 3.

Answered by bobhans last updated on 09/Jul/20

(a) 2^7  = 128  (b) 2^7 −1=127  (e) C_3 ^7  = ((7×6×5)/(3×2×1)) = 35

Commented byCynosure last updated on 08/Jul/20

(d) should not be 35 sir

Commented byRasheed.Sindhi last updated on 08/Jul/20

(d)Nonempty proper subsets          128−2=126

Commented byRasheed.Sindhi last updated on 08/Jul/20

Typo in 3rd line  (e) C_3 ^7  = ((7×6×5)/(3×2×1)) = 35

Commented bybobhans last updated on 09/Jul/20

yes sir. thank you

Answered by bemath last updated on 09/Jul/20

(f){1,2} ⇒1  {1,2,_}⇒C_1 ^5  = 5  {1,2,_,_}⇒C_2 ^5  = 10  {1,2,_,_,_}⇒C_3 ^5  = 10  {1,2,_,_,_,_}⇒C_4 ^5  = 5  {1,2,_,_,_,_,_}⇒C_5 ^5  = 1  totally 32