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-Subs

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

f o r A = {1, 2, 3, 4, 5, 6, 7}, c o m p u t e t h e n u m b e r o f :

(a) S u b s e t s o f A .

(b) N o n e m p t y s u b s e t s o f A .

(c) p r o p e r s u b s e t s o f A .

(d) N o n e m p t y p r o p e r s u b s e t o f A .

(e) S u b s e t s o f A c o n t a i n i n g t h r e e e l e m e n t .

(f) S u b s e t s o f A c o n t a i n i n g 1, 2 .

(g) P r o p e r s u b s e t s o f A c o n t a i n i n g 1, 2 .

(h) S u b s e t o f A w i t h a n e v e n n u m b e r o f e l e m e n t .

(i) S u b s e t o f A w i t h a n o d d n u m b e r o f e l e m e n t .

(j) S u b s e t s o f A w i t h a n o d d n u m b e r o f e l e m e n t s, i n c l u d i n g t h e e l e m e n t 3 .

Answered by bobhans last updated on 09/Jul/20

(a) 2^{7} = 128

(b) 2^{7} - 1 = 127

(e) C_{3}^{7} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

Commented by Cynosure last updated on 08/Jul/20

(d) s h o u l d n o t b e 35 s i r

Commented by Rasheed.Sindhi last updated on 08/Jul/20

(d) N o n e m p t y p r o p e r s u b s e t s

128 - 2 = 126

Commented by Rasheed.Sindhi last updated on 08/Jul/20

T y p o i n 3 r d l i n e

(e) C_{3}^{7} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

Commented by bobhans last updated on 09/Jul/20

y e s s i r . t h a n k y o u

Answered by bemath last updated on 09/Jul/20

(f) {1, 2} \Rightarrow 1

{1, 2,_} \Rightarrow C_{1}^{5} = 5

{1, 2,_,_} \Rightarrow C_{2}^{5} = 10

{1, 2,_,_,_} \Rightarrow C_{3}^{5} = 10

{1, 2,_,_,_,_} \Rightarrow C_{4}^{5} = 5

{1, 2,_,_,_,_,_} \Rightarrow C_{5}^{5} = 1

t o t a l l y 32

Facebook Tweet Pin