Answer to Question #286850 in Discrete Mathematics for Pearls

Question #286850

Each of 39 of my friends has either a dog a cat or a rabbit each of 24 of them has a dog each of 17 gas a cat and each of 16 has a rabbit the number having both a dog and a cat is one more than the number having both a cat and a rabbit while 2of them have all the three how many of my friends have both a rabbit and cat


1
Expert's answer
2022-01-12T18:42:14-0500

Each of 39 of my friends has either a dog, a cat or a rabbit. Each of 24 of them has a dog, each of 17 has a cat and each of 16 has a rabbit. The number having both a dog and a cat is 1 more than the number having both a cat and a rabbit. There are 9 who have both a dog and a rabbit while 2 of them have all the three. How many of my friends have both a rabbit and a cat?

Let x=x= the number having both a cat and a rabbit. Then x+1=x+1= the number having both a dog and a cat.


N(DCR)=N(D)+N(C)+N(R)N(D\cup C\cup R)=N(D)+N(C)+N(R)

N(DC)N(DR)N(CR)-N(D\cap C)-N(D\cap R)-N(C\cap R)

+N(DCR)+N(D\cap C\cap R)

39=24+17+16(x+1)x9+239=24+17+16-(x+1)-x-9+2

2x=102x=10

x=5x=5

There are 5 who have both a rabbit and a cat.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment