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 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 .