Question

10. Last February had 28 days and each night in that month Maria had a dream. Some of her dreams involved dogs, some involved cats and some involved no animals at all. You are given that 16 involved dogs, 15 involved cats and 4 involved no animals at all. How many of Maria's dreams involved BOTH dogs and cats?

(A) 3
(B) 5
(C) 7
(D) 9
(E) 11​

Answer 1

To determine how many of Maria's dreams involved both dogs and cats, we use the principle of inclusion-exclusion, leading us to the answer of 3 dreams featuring both animals.Therefore correct option is A

Step-by-step explanation:

The question involves solving a classic problem in set theory, often tackled using Venn diagrams. Maria had 28 dreams in February. According to the problem, 16 of these dreams involved dogs, 15 involved cats, and 4 involved no animals at all.

To find out how many of her dreams involved BOTH dogs and cats, we can use the principle of inclusion-exclusion. Here are the steps:

1. Add the total number of dreams involving dogs to those involving cats: 16 + 15 = 31.
2. Subtract the total number of dreams (28 days) from this sum to account for the overlap: 31 - 28 = 3.
3. The result (3) represents the number of dreams in which both dogs and cats appeared.

So, the answer to the question is (A) 3.