if two finite sets have m and n term.if the no of subset of first set is 112 more then the no of subset of second set.find m and n?


Question and Answers Forum

All Questions Topic List
Arithmetic Questions
Previous in All Question Next in All Question
Previous in Arithmetic Next in Arithmetic
Question Number 69175 by Aditya789 last updated on 21/Sep/19

$i f t w o f i n i t e s e t s h a v e m a n d n t e r m . i f t h e n o o f s u b s e t o f f i r s t s e t i s 112 m o r e t h e n t h e n o o f s u b s e t o f s e c o n d s e t . f i n d m a n d n ?$
	Answered by Rasheed.Sindhi last updated on 21/Sep/19

	$∣ A ∣= m, ∣ B ∣= n$ $P (A) = 2^{m}, P (B) = 2^{n}$ $P (A) - P (B) = 2^{m} - 2^{n} = 112$ $2^{m} ⩾ 2^{7} \Rightarrow m ⩾ 7$ $2^{n} = 2^{m ⩾ 7} - 112$ $F o r m = 7$ $2^{n} = 2^{7} - 112 = 16 = 2^{4} \Rightarrow n = 4$ $O n e s o l u t i o n : (7, 4)$ $I h a v e f o u n d o u t o n e s o l u t i o n b u t I$ $I^{'} m n o t c e r t a i n o f i t s u n i q u e n e s s .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum