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.


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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
	$(f){1,2} ⇒1 {1,2,_}⇒C_1 ^5 = 5 {1,2,_,_}⇒C_2 ^5 = 10 {1,2,_,_,_}⇒C_3 ^5 = 10 {1,2,_,_,_,_}⇒C_4 ^5 = 5 {1,2,_,_,_,_,_}⇒C_5 ^5 = 1 totally 32$
	$(f) {1, 2} \Rightarrow 1$ ${1, 2,_} \Rightarrow C_{1}^{5} = 5$ ${1, 2,_,_} \Rightarrow C_{2}^{5} = 10$ ${1, 2,_,_,_} \Rightarrow C_{3}^{5} = 10$ ${1, 2,_,_,_,_} \Rightarrow C_{4}^{5} = 5$ ${1, 2,_,_,_,_,_} \Rightarrow C_{5}^{5} = 1$ $t o t a l l y 32$
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