Question

Discrete Structures problem

QUESTION 5 50% of Americans like brocolli, 63% of Americans like cauliflower, and 31% of Americans like both brocolli and cauliflower. What percentage of Americans like neither vegetable? QUESTION 6 There are twelve houses on a street we wish to canvass. Seven houses are on the left side of the street and five houses are on the right. We will select a subset of four houses to visit, such that at least one house from each side of the street is included. How many such subsets can we select?

Answer 1

Criven 50% of Americans like Brocolli 639. of American like Caulitower 3 110 of Americans like both Bercoullin and Cauli Hower. To find AD13 z oo oo | Al=1 / 10 2 Sol live. A z 50% like Brocoli Alz 50 a 3 100 | Alz 0-5 like Brocoli Bz 63% like caulifloroes Bl= 63 100

100 100 + ( we knolo This for 100 100 100 -31% 100 lanB = 31% like Broldi and ccullione Ön l'Ble 0.63 or 63 like Cauliflower @ lanBl=31 Nowhets. Us 1st determine the Americans who like either brocoli Cauliflower or both JAUB) = 141+IB? - ANB] TAUBI= 50 +63 31 Or LAUB < 50%+63% IA UBI .82 or (AUB) =827. LAUB) 1-1 AUBI (we know 21 1-82 complement formula | AUD 18 0x TAUB 1-82). 100 1 - 82100 184. > (Does not like any) So 18% Americans do not like any of the Conclusion of question 5 18% of 'Americans like neither vegetable (6) Given » Total houses a la 7 house on left side of sheet sheel 100 2 LAUB) 2 regetables Right side of

ری we s. So is Rig -D we Side 1 we are given 12 houses. telt I house on left on sheet. B! 3 5. house on R Right of sheet wool select a subred of 4 houses such that at least 1 house from each of the shree ps included we have to select a subsed of 4 house Atleast means $ 3. so atleast a house from each side of sheet we can select as. (0 s 2 house of left 2 house of 3 house of left , house of Right? @s { 1 house of left 3 house of Right 12 Tolat subsets + We 90+ are 3 pright so we can select as (į 1,2,3,43 {1,3,5,43 Total (3) is 3 { 1,2,4,63 (4) So we got total 3 subsets of thouses so we can select 3 such subsets of 4 hauses such that we select alleast one house from each side of Steel Right? 2 2 (2) / 9 3 5 9 41 deft of + 10 2 4 6 10 PLEASE DO UPVOTE: THANK YOU ( 2 Conclusion GENERACIONS INTERCEPTAINEET Tamm