I know I posted this already but there is a typo.

There are 49 mice in a pet shop.
30 mice are white.
27 mice are male.
18 mice have short tails.
8 mice are white and have short tails.
11 mice are male and have short tails.
7 mice are male but neither white nor short-tailed.
5 mice have all three characteristics and
2 have none.

Note:
W represents white mice
M represents male mice
S represents short-failed mice

I made a venn diagram but need help on...
n(M' U S)
The answer says 22+18-7=33
I know that M' means 49-27=22 and the union sign means add the 18 short tails but where does 7 come from? I know you have to subtract the overlap but according to my Venn diagram, the overlap between M and D is 5+6=11.

To find the answer to the expression "n(M' U S)" and understand why it's 33, let's break it down step by step.

First, let's define the terms:
- M' represents the complement of M, which means all mice that are not male. So, M' = 49 - 27 = 22.
- U symbolizes the union of two sets, which means combining all elements from both sets without duplication.
- S represents the set of mice with short tails, and we know that S = 18.

To calculate "n(M' U S)", we need to combine the elements from the two sets, M' and S, without duplication.

Now, let's consider the overlap you mentioned: 5 for mice that are white, male, and have short tails, and 6 for mice that are male, short-tailed, but neither white nor included in the previous 5.

Here's how we can get the final answer:

1. Start with M', which is 22.
2. Add the number of mice with short tails (S), which is 18.
22 + 18 = 40.

At this point, we have considered all the mice that are not male or have short tails. However, we need to subtract the overlapping mice since they were counted twice: once in M' and once in S.

3. Subtract the number of mice that are both male and have short tails, which is 7.
40 - 7 = 33.

Thus, the final answer is 33 for the expression "n(M' U S)".

Regarding the overlap you mentioned in your Venn diagram, the 11 mice represent the combined count of mice with all three characteristics (5) plus the count of mice that are male, short-tailed, but neither white nor included in the previous 5 (6). However, in this case, we are only considering the count of mice that are not male (M') or have short tails (S). So, the overlap we need to subtract is 7, which is the number of mice that have both characteristics.

I hope this clears up any confusion and helps you understand how to arrive at the answer of 33 for "n(M' U S)".

To find the value of n(M' U S), we need to determine the number of mice that are either not male or have short tails.

Let's break it down step-by-step:

1. We know that there are 49 mice in total, 27 of which are male (M'). So, the number of mice that are not male is M = 49 - 27 = 22.

2. We also know that there are 18 mice with short tails (S).

3. To find the union of M' (not male) and S, we add the number of mice in M' (22) to the number of mice in S (18):
n(M' U S) = 22 + 18 = 40.

4. However, we need to account for the overlap between male and short-tailed mice, which is counted twice in our initial calculation. The overlap is given by 11 mice (the number of mice that have all three characteristics).

5. Therefore, we need to subtract the overlap (11) from the previous result:
n(M' U S) = 40 - 11 = 29.

So, according to the given information, the correct value for n(M' U S) is 29, not 33 as mentioned in your answer key.